共查询到20条相似文献,搜索用时 62 毫秒
1.
Tamar Burak 《Israel Journal of Mathematics》1972,12(1):79-93
Let A be the closed unbounded operator inL
p(G) that is associated with an elliptic boundary value problem for a bounded domainG. We prove the existence of a spectral projectionE determined by the set Γ = {λ;θ
1≦argλ≦θ
2} and show thatAE is the infinitesimal generator of an analytic semigroup provided that the following conditions hold: 1<p<∞; the boundary
ϖΓ of Γ is contained in the resolvent setp(A) ofA;π/2≦θ<θ
2≦3π/2 ; and there exists a constantc such that (I)││(λ-A)-1││≦c/│λ│ for λ∈ϖΓ. The following consequence is obtained: Suppose that there exist constantsM andc such that λ∈p(A) and estimate (I) holds provided that |λ|≧M and Re λ=0. Then there exist bounded projectionE
− andE
+ such thatA is completely reduced by the direct sum decompositionL
p(G)=E−Lp (G) ⊕E+Lp (G) and each of the operatorsAE
− and—AE
+ is the infinitestimal generator of an analytic semigroup. 相似文献
2.
Suppose λ is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal functionL
λ(x)
x∈R, satisfying the interpolatory conditionsL
k = δ0k,k∈Z
. One objective of this paper is to derive several additional properties ofL
λ. For example, it is shown thatL
λ possesses the signregularity property sgn[L
λ(x)]=sgn[sin(πx)/(πx)],x∈R, and that |L
λ (x)|≤2e
8 min {(⌊|x|⌋+1)-1,exp(-λ⌊|x|⌋)},x∈R. The analysis is based on a simple representation formula forL
λ and employs some methods from classical function theory. A second consideration in the paper is the Gaussian cardinal-interpolation
operatorL
λ, defined by the equation (L
λy)(x):=
,x∈R, y=(yk)k∈Z. On account of the exponential decay of the cardinal functionL
λ,L
λ is a well-defined linear map froml
∞ (Z) intoL
∞ (R). Its associated operatornorm ‖L
λ‖ is called the Lebesgue constant ofL
λ. The latter half of the paper establishes the following estimates for the Lebesgue constant: ‖L
λ‖≍1, λ→∞, and ║Lλ║≍log(1/λ), λ→0+. Suitable multidimensional analogues of these results are also given.
For Carl de Boor, on the occasion of his sixtieth birthday 相似文献
3.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献
4.
Michael Lin 《Israel Journal of Mathematics》1982,42(4):300-308
We prove the local ergodic theorem inL
∞: Let {T
t}t>0 be a strongly continuous semi-group of positive operators onL
1. IfT
t is continuous at 0, then ɛ−1∫
0
F
T
1
*
f(x)dt→T
0
*
f(x) a.e., for everyf∈L
∞. The technique shows how to obtain theL
p local ergodic theorems from theL
1-contraction case. It applies also to differentiation ofL
p additive processes. Then-dimensional case, which is new, is proved by reduction to then-dimensionalL
1-contraction case, solved by M. Akcoglu and A. del Junco.
Research carried out during a sabbatical leave at the Ohio State University. 相似文献
5.
René L. Schilling 《Probability Theory and Related Fields》1998,112(4):565-611
Let (A,D(A)) be the infinitesimal generator of a Feller semigroup such that C
c
∞(ℝ
n
)⊂D(A) and A|C
c
∞(ℝ
n
) is a pseudo-differential operator with symbol −p(x,ξ) satisfying |p(•,ξ)|∞≤c(1+|ξ|2) and |Imp(x,ξ)|≤c
0Rep(x,ξ). We show that the associated Feller process {X
t
}
t
≥0 on ℝ
n
is a semimartingale, even a homogeneous diffusion with jumps (in the sense of [21]), and characterize the limiting behaviour
of its trajectories as t→0 and ∞. To this end, we introduce various indices, e.g., β∞
x
:={λ>0:lim
|ξ|→∞
|
x
−
y
|≤2/|ξ||p(y,ξ)|/|ξ|λ=0} or δ∞
x
:={λ>0:liminf
|ξ|→∞
|
x
−
y
|≤2/|ξ|
|ε|≤1|p(y,|ξ|ε)|/|ξ|λ=0}, and obtain a.s. (ℙ
x
) that lim
t
→0
t
−1/λ
s
≤
t
|X
s
−x|=0 or ∞ according to λ>β∞
x
or λ<δ∞
x
. Similar statements hold for the limit inferior and superior, and also for t→∞. Our results extend the constant-coefficient (i.e., Lévy) case considered by W. Pruitt [27].
Received: 21 July 1997 / Revised version: 26 January 1998 相似文献
6.
By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple
positive solutions for the third-order threepoint singular semipositone BVP:
where 1/2 < η < 1, the non-linear term ƒ(t, x): (0, 1) × (0, + ∞) → (-∞, + ∞) is continuous and may be singular att = 0,t = 1, andx = 0, also may be negative for some values oft andx, λ is a positive parameter. 相似文献
7.
Chen Hua 《数学学报(英文版)》1991,7(1):38-50
In this paper, I study the microlocal hypoellipticity for a class of totally characteristic operators (1.1). My main result
is as follows:
Under the conditions (I), (II), if the indicial operator of (1.1) is microlocally hypoelliptic in the complement ofWF
x(Pu(t,·)) for anyu(t,x)∈C
b
∞
([0,T], ℰ),t∈[0,T], λ∈ℤ, then the operator (1.1) is microlocally hypoelliptic in the variablex.
Supported by the Natural Science Foundation and Young Men's Science Foundation of Academia Sinica 相似文献
8.
R. Crescimbeni R. A. Macías T. Menárguez J. L. Torrea B. Viviani 《Journal of Evolution Equations》2009,9(1):81-102
The ρ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. Δ and −Δ + |x|2) are proved to be bounded from into itself (from into weak- in the case p = 1) for 1 ≤ p < ∞ and w being a weight in the Muckenhoupt’s A
p
class. In the case p = ∞ it is proved that these operators do not map L
∞ into itself. Even more, they map L
∞ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.
R. Crescimbeni was partially supported by Fundación Carolina, Ministerio de Educación de la República Argentina and Universidad
Nacional del Comahue. R. A. Macías and B. Viviani were partially supported by Facultad de Ingeniera Química-UNL. 相似文献
9.
Jerk Matero 《manuscripta mathematica》1996,91(1):379-391
Assume that Ω is a bounded, strictly convex, smooth domain in ℝN withN≥2. We consider the problem det ((∂
iju(x)))=f(x,u(x)),u(x)→∞ asx→∂Ω, where (∂
iju(x)) denotes the Hessian ofu(x) andf meets some natural regularity and growth conditions. We prove that there exists a unique smooth, strictly convex solution
of this problem. The boundary-blow-up rate ofu(x) is characterized in terms of the distance ofx from ∂Ω.
Partially supported by the Royal Swedish Academy of Sciences, Gustaf Sigurd Magnuson's fund. 相似文献
10.
Walter Feit 《Israel Journal of Mathematics》1983,46(4):274-300
Let χ be an irreducible character of a finite groupG. Letp=∞ or a prime. Letm
p (χ) denote the Schur index of χ overQ
p
, the completion ofQ atp. It is shown that ifx is ap′-element ofG such that
for all irreducible charactersX
u ofG thenm
p (χ)/vbχ(x). This result provides an effective tool in computing Schur indices of characters ofG from a knowledge of the character table ofG. For instance, one can read off Benard’s Theorem which states that every irreducible character of the Weyl groupsW(E
n), n=6,7,8 is afforded by a rational representation. Several other applications are given including a complete list of all
local Schur indices of all irreducible characters of all sporadic simple groups and their covering groups (there is still
an open question concerning one character of the double cover of Suz).
This work was partly supported by NSF Grant MCS-8201333. 相似文献
11.
Shu-Leung Tang 《manuscripta mathematica》1993,81(1):379-386
LetK be an imaginary quadratic field andp an odd prime which splits inK. We study the Iwasawa invariants for ℤ
p
-extensions ofK. This is motivated in part by a recent result of Sands. The main result is the following. Assumep does not divide the class number ofK. LetK
∞ be a ℤ
p
-extension ofK. SupposeK
∞ is not totally ramified at the primes abovep. Then the μ-invariant forK
∞/K vanishes. We also show that if μ=0 for all ℤ
p
-extensions ofK, then the λ-invariant is bounded asK
∞ runs through all such extensions. 相似文献
12.
Uri Fixman 《Integral Equations and Operator Theory》2000,37(1):9-19
LetA be the linear operator inL
p
(0, 1), 1<p<∞,p≠2, defined by
,x∈L
p
(0, 1),s∈[0,1]. We show that the real values of numbers in the numerical range ofA have maximum
, whereq=p/(p−1). This amounts to an inequality between integrals, for which we determine the case of equality. 相似文献
13.
Marcinkiewicz Integrals with Non-Doubling Measures 总被引:2,自引:0,他引:2
Let μ be a positive Radon measure on
which may be non doubling. The only condition that μ must satisfy is μ(B(x, r)) ≤ Cr
n
for all
, r > 0 and some fixed constants C > 0 and n ∈ (0, d]. In this paper, we introduce the Marcinkiewicz integral related to a such measure with kernel satisfying some H?rmander-type
condition, and assume that it is bounded on L
2(μ). We then establish its boundedness, respectively, from the Lebesgue space L
1(μ) to the weak Lebesgue space L
1,∞(μ), from the Hardy space H
1(μ) to L
1(μ) and from the Lebesgue space L
∞(μ) to the space RBLO(μ). As a corollary, we obtain the boundedness of the Marcinkiewicz integral in the Lebesgue space L
p
(μ) with p ∈ (1,∞). Moreover, we establish the boundedness of the commutator generated by the RBMO(μ) function and the Marcinkiewicz integral with kernel satisfying certain slightly stronger H?rmander-type condition, respectively,
from L
p
(μ) with p ∈ (1,∞) to itself, from the space L log L(μ) to L
1,∞(μ) and from H
1(μ) to L
1,∞(μ). Some of the results are also new even for the classical Marcinkiewicz integral.
The third (corresponding) author was supported by National Science Foundation for Distinguished Young Scholars (No. 10425106)
and NCET (No. 04-0142) of China. 相似文献
14.
Quanhua Xu 《Israel Journal of Mathematics》1995,91(1-3):173-187
Let (Ω,F, P) be a probability space and {F
n}n≥0 a regular increasing sequence of sub-σ-fields ofF. LetH
1(Ω) be the usual Hardy space ofF
n-martingales. We show that the couple (H
1(Ω),L
∞(Ω)) is a partial retract of (L
1(Ω),L
∞(Ω)). It is also proved that (L
p(Ω),BMO(Ω)) is a partial retract of (L
p(Ω),L
∞(Ω)) for all 1<p<∞. 相似文献
15.
Let (ℋ
t
)
t≥0 be the Ornstein–Uhlenbeck semigroup on ℝ
d
with covariance matrix I and drift matrix λ(R−I), where λ>0 and R is a skew-adjoint matrix, and denote by γ
∞ the invariant measure for (ℋ
t
)
t≥0. Semigroups of this form are the basic building blocks of Ornstein–Uhlenbeck semigroups which are normal on L
2(γ
∞). We prove that if the matrix R generates a one-parameter group of periodic rotations, then the maximal operator ℋ*
f(x)=sup
t≥o
|ℋ
t
f(x)| is of weak type 1 with respect to the invariant measure γ
∞. We also prove that the maximal operator associated to an arbitrary normal Ornstein–Uhlenbeck semigroup is bounded on L
p
(γ
∞) if and only if 1<p≤∞.
相似文献
16.
We present a homological principle that governs the behaviour of couples of exact sequences of quasi-Banach spaces. Three
applications are given: (i) A unifying method of proof for the results of Lindenstrauss, Rosenthal, Kalton, Peck and Kislyakov
about the extension and lifting of isomorphisms inc
0,ι
∞,ι
p
andL
pfor 0<p≤1; (ii) A study of the Dunford-Pettis property in duals of quotients ofL
∞-spaces; and (iii) New results on the extension ofC(K)-valued operators.
The research has been supported in part by DGICYT project BFM 2001-0813. 相似文献
17.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):135-140
Summary LetF be a distribution function over the real line. DefineR
p(y)=∫|x−y|pdF(x) forp≧1. Forp>1 there is a unique minimizer ofR
p(·), sayγ
p. Under mild conditions onF it is shown that
exists and that the limit is a median. Thus, one could use this limit as a definition of a unique median. Also it is shown
that
whereR is the right extremity ofF andL is the left extremity ofF provided that −∞<L≦R<∞. A similar result is available ifL=−∞,R=∞, yetF has symmetric tails. 相似文献
18.
We study the Cauchy problem for the nonlinear dissipative equations (0.1) uo∂u-αδu + Β|u|2/n
u = 0,x ∃ Rn,t } 0,u(0,x) = u0(x),x ∃ Rn, where α,Β ∃ C, ℜα 0. We are interested in the dissipative case ℜα 0, and ℜδ(α,Β)≥ 0, θ = |∫ u0(x)dx| ⊋ 0, where δ(α, Β) = ##|α|n-1nn/2 / ((n + 1)|α|2 + α2
n/2. Furthermore, we assume that the initial data u0 ∃ Lp are such that (1 + |x|)αu0 ∃ L1, with sufficiently small norm ∃ = (1 + |x|)α u0 1 + u0 p, wherep 1, α ∃ (0,1). Then there exists a unique solution of the Cauchy problem (0.1)u(t, x) ∃ C ((0, ∞); L∞) ∩ C ([0, ∞); L1 ∩ Lp) satisfying the time decay estimates for allt0 u(t)||∞ Cɛt-n/2(1 + η log 〈t〉)-n/2, if hg = θ2/n 2π ℜδ(α, Β) 0; u(t)||∞ Cɛt-n/2(1 + Μ log 〈t〉)-n/4, if η = 0 and Μ = θ4/n 4π)2 (ℑδ(α, Β))2 ℜ((1 + 1/n) υ1-1 υ2) 0; and u(t)||∞ Cɛt-n/2(1 + κ log 〈t〉)-n/6, if η = 0, Μ = 0, κ 0, where υl,l = 1,2 are defined in (1.2), κ is a positive constant defined in (2.31). 相似文献
19.
James Olsen 《Israel Journal of Mathematics》1972,11(1):1-13
The principal result of this paper is that the convex combination of two positive, invertible, commuting isometries ofL
p(X,F, μ) 1<p<+∞, one of which is periodic, admits a dominated estimate with constantp/p−1. In establishing this, the following analogue of Linderholm’s theorem is obtained: Let σ and ε be two commuting non-singular
point transformations of a Lebesgue Space with τ periodic. Then given ε>O, there exists a periodic non-singular point transformation σ′ such that σ′ commutes with τ and μ(x:σ′x≠σx}<ε. Byan approximation argument, the principal result is applied to the convex combination of two isometries ofL
p (0, 1) induced by point transformations of the form τx=x
k,k>0 to show that such convex combinations admit a dominated estimate with constantp/p−1.
Research supported in part by NSF Grant No. GP-7475. A portion of the contents of this paper is based on the author’s doctoral
dissertation written under the direction of Professor R. V. Chacon of the University of Minnesota. 相似文献
20.
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 相似文献