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1.
S Thangavelu 《Proceedings Mathematical Sciences》1990,100(2):147-156
The uniform boundedness of the Riesz means for the sublaplacian on the Heisenberg groupH
n is considered. It is proved thatS
R
α
are uniformly bounded onL
p(Hn) for 1≤p≤2 provided α>α(p)=(2n+1)[(1/p)−(1/2)]. 相似文献
2.
Boris Rubin 《Journal d'Analyse Mathématique》1999,77(1):105-128
Explicit inversion formulas are obtained for the hemispherical transform(FΜ)(x) = Μ{y ∃S
n :x. y ≥ 0},x ∃S
n, whereS
n is thendimensional unit sphere in ℝn+1,n ≥ 2, and Μ is a finite Borel measure onS
n. If Μ is absolutely continuous with respect to Lebesgue measuredy onS
n, i.e.,dΜ(y) =f(y)dy, we write(F f)(x) = ∫
x.y> 0
f(y)dy and consider the following cases: (a)f ∃C
∞(Sn); (b)f ∃ Lp(S
n), 1 ≤ p < ∞; and (c)f ∃C(Sn). In the case (a), our inversion formulas involve a certain polynomial of the Laplace-Beltrami operator. In the remaining
cases, the relevant wavelet transforms are employed. The range ofF is characterized and the action in the scale of Sobolev spacesL
p
γ
(Sn) is studied. For zonalf ∃ L1(S
2), the hemispherical transformF f was inverted explicitly by P. Funk (1916); we reproduce his argument in higher dimensions.
Partially sponsored by the Edmund Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation
(Germany). 相似文献
3.
Limin Sun 《Arkiv f?r Matematik》1995,33(1):173-182
Let Δ be the Laplace-Beltrami operator on ann dimensional completeC
∞ manifoldM In this paper we establish an estimate ofe
tΔ
(dμ) valid for allt>0 wheredμ is a locally uniformly α dimensional measure onM 0≤α≤n The result is used to study the mapping properties of (I-tΔ)-β considered as an operator fromL
p
(M dμ) toL
p
(M dx) wheredx is the Riemannian measure onM β>(n−α)/2p′ 1/p+1/p′=1 1≤p≤∞ 相似文献
4.
We consider singular integral operators of the form (a)Z
1L−1Z2, (b)Z
1Z2L−1, and (c)L
−1Z1Z2, whereZ
1 andZ
2 are nonzero right-invariant vector fields, andL is theL
2-closure of a canonical Laplacian. The operators (a) are shown to be bounded onL
p for allp∈(1, ∞) and of weak type (1, 1), whereas all of the operators in (b) and (c) are not of weak type (p, p) for anyp∈[1, ∞).
Research supported by the Australian Research Council.
Research carried out as a National Research Fellow. 相似文献
5.
Fred B. Weissler 《Israel Journal of Mathematics》1981,38(1-2):29-40
The existence and non-existence of global solutions and theL
p blow-up of non-global solutions to the initial value problemu′(t)=Δu(t)+u(t)
γ
onR
n are studied. We consider onlyγ>1. In the casen(γ − 1)/2=1, we present a simple proof that there are no non-trivial global non-negative solutions. Ifn(γ−1)/2≦1, we show under mild technical restrictions that non-negativeL
p solutions always blow-up inL
p norm in finite time. In the casen(γ−1)/2>1, we give new sufficient conditions on the initial data which guarantee the existence of global solutions.
Research partially supported by NSF grant MCS79-03636. 相似文献
6.
Usha N. Bhosle 《Proceedings Mathematical Sciences》2005,115(4):445-451
LetM be the moduli space of generalized parabolic bundles (GPBs) of rankr and degree dona smooth curveX. LetM
−L
be the closure of its subset consisting of GPBs with fixed determinant− L. We define a moduli functor for whichM
−L
is the coarse moduli scheme. Using the correspondence between GPBs onX and torsion-free sheaves on a nodal curveY of whichX is a desingularization, we show thatM
−L
can be regarded as the compactified moduli scheme of vector bundles onY with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves
with a fixed determinant in the moduli space of torsion-free sheaves onY. The relation to Seshadri-Nagaraj conjecture is studied. 相似文献
7.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
8.
On Linearly Isometric Extensions for 1-Lipschitz Mappings Between Unit Spheres of ALP-spaces (p 〉 2)
In this paper, we show that if Vo is a 1-Lipschitz mapping between unit spheres of two ALP-spaces with p 〉 2 and -Vo(S1(LP)) C Vo(S1(LP)), then V0 can be extended to a linear isometry defined on the whole space. If 1 〈 p 〈 2 and Vo is an "anti-l-Lipschitz" mapping, then Vo can also be linearly and isometrically extended. 相似文献
9.
Blending methods of Topological Dynamics and Control Theory, we develop a new technique to construct compact-Lie-group-valued
minimal cocycles arising as fundamental matrix solutions of linear differential equations with recurrent coefficients subject
to a given constraint. The precise requirement on the coefficients is that they belong to a specified closed convex subsetS of the Lie algebraL of the Lie group. Our result is proved for a very thin class of cocycles, since the dimension ofS is allowed to be much smaller than that ofL, and the only assumption onS is thatL
0(S) =L, whereL
0(S) is the ideal ofL(S) generated by the difference setS − S, andL(S) is the Lie subalgebra ofL generated byS. This covers a number of differential equations arising in Mathematical Physics, and applies in particular to the widely
studied example of the Rabi oscillator.
Supported in part by a Research Council grant from Rutgers University.
Supported in part by NSF Grant DMS92-02554. 相似文献
10.
Let L be the infinitesimal generator of an analytic semigroup on L2 (Rn) with suitable upper bounds on its heat kernels. Assume that L has a bounded holomorphic functional calculus on L2(Rn). In this paper,we define the Littlewood- Paley g function associated with L on Rn × Rn, denoted by GL(f)(x1, x2), and decomposition, we prove that ‖SL(f)‖p ≈‖GL(f)‖p ≈‖f‖p for 1 < p <∞. 相似文献
11.
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
12.
K-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex
Song Li 《数学学报(英文版)》1999,15(3):395-406
An inverse theorem for the best weighted polynomial approximation of a function in
(S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial
approximation in
, wherew
α is a Jacobi-type weight onS, 0<p ≤ ∞,S is a simplex andW
λ is a Freud weight. For Ditzian-TotikK-functionals onL
p(S), 1 ≤p ≤ ∞, we obtain a new equivalence expression. 相似文献
13.
Rainer Wittmann 《Israel Journal of Mathematics》1987,59(1):8-28
LetT be a positive linear contraction inL
p (1≦p<∞), then we show that lim ‖T
pf −T
n+1
f‖
p
≦(1 − ε)21/p
(f∈L
p
+
, ε>0 independent off) implies already limn
n→∞ ‖T
nf −T
n+1
n+1f ‖p
p=0. Several other related results as well as uniform variants of these are also given. Finally some similar results inLsu/t8 andC(X) are shown. 相似文献
14.
Loren D. Pitt 《Israel Journal of Mathematics》1976,24(2):94-118
For a fixed weight Δ(dx) onR
1 and a linear space ℋ ⊆L
p(Δ) of entire functions that is closed under difference quotientsh(·)→(z−·)
−1[h(z)−h(·)], theL
p(Δ) closure
of ℋ is studied and characterized in terms of the normsL(z), (z∈C
1 of the evaluation functionalsh→h(z),h∈ℋ.
Partially supported by DA-ARO-31-124-71-6182 and NSF GP-43011. 相似文献
15.
Vladimir Shpilrain 《Israel Journal of Mathematics》1995,91(1-3):307-316
LetE be a bounded Borel subset of ℝn,n≥2, of positive Lebesgue measure andP
E the corresponding ‘Pompeiu transform”. We prove thatP
E is injective onL
p(ℝn) if 1≤p≤2n/(n-1). We explore the connection between this problem and a Wiener-Tauberian type theorem for theM(n) action onL
q(ℝn) for various values ofq. We also take up the question of whenP
E is injective in caseE is of finite, positive measure, but is not necessarily a bounded set. Finally, we briefly look at these questions in the
contexts of symmetric spaces of compact and non-compact type. 相似文献
16.
Let L
p
(S), 0 < p < +∞, be a Lebesgue space of measurable functions on S with ordinary quasinorm ∥·∥
p
. For a system of sets {B
t
|t ∈ [0, +∞)
n
} and a given function ψ: [0, +∞)
n
↦ [ 0, +∞), we establish necessary and sufficient conditions for the existence of a function f ∈ L
p
(S) such that inf {∥f − g∥
p
p
g ∈ L
p
(S), g = 0 almost everywhere on S\B
t
} = ψ (t), t ∈ [0, +∞)
n
. As a consequence, we obtain a generalization and improvement of the Dzhrbashyan theorem on the inverse problem of approximation
by functions of the exponential type in L
2.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1116–1127, August, 2006. 相似文献
17.
Guido Cortesani 《Annali dell'Universita di Ferrara》1997,43(1):27-49
Let Ω be an open and bounded subset ofR
n
with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R
m
) whose jump setS
vis essentially closed and polyhedral and which are of classW
k, ∞ (S
v,R
m) for every integerk are strongly dense inGSBV
p(Ω,R
m
), in the sense that every functionu inGSBV
p(Ω,R
m
) is approximated inL
p(Ω,R
m
) by a sequence of functions {v
k{j∈N with the described regularity such that the approximate gradients ∇v
jconverge inL
p(Ω,R
nm
) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS
v
j converges to the (n−1)-dimensional measure ofS
u. The structure ofS
v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneu∈GSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.相似文献
18.
WANG Meng CHEN Jiecheng & FAN Dashan Department of Mathematics Zhejiang University 《中国科学A辑(英文版)》2006,49(1):98-108
We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog L(Sn-1 × Sm-1) satisfying the cancellation condition. 相似文献
19.
In this paper,we obtain the boundedness of the parabolic singular integral operator T with kernel in L(logL)1/γ(Sn-1) on Triebel-Lizorkin spaces.Moreover,we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q(f) from ∥f∥ F˙p0,q(Rn) into Lp(Rn). 相似文献
20.
Elena Rubei 《Annali dell'Universita di Ferrara》2004,50(1):151-165
This paper deals with syzygies of the ideals of the Veronese embeddings. By Green’s Theorem we know thatO
P
n
(d) satisfies Green-Lazarsfeld’s PropertyN
p ∀d≥p, ∀n. By Ottaviani-Paoletti’s theorem ifn≥2, d≥3 and 3d−2≤p thenO
P
n
(d) does not satisfy PropertyN
p. The casesn≥3, d≥3, d<p<3d−2 are still open (exceptn=d=3). Here we deal with one of these cases, namely we prove thatO
P
n
(3) satisfies PropertyN
4 ∀n. Besides we prove thatO
P
n
(d) satisfiesN
p ∀n≥p iffO
P
n
(d) satisfiesN
p.
Sunto L’argomento di questo articolo sono le sizigie degli ideali delle varietà di Veronese. Per il teorema di Green sappiamo cheO P n (d) soddisfa la proprietàN p di Green-Lazarsfeld ∀d≥p, ∀n. Per il teorema di Ottaviani-Paoletti sen≥2, d≥3 and 3d−2≤p alloraO P n (d) non soddisfa la ProprietàN p. I casin≥3, d≥3, d<p<3d−2 sono ancora aperti (eccetton=d=3). Qui consideriamo uno di tali casi, precisamente proviamo cheO P n (3) soddisfa la ProprietàN 4 ∀n. Inoltre proviamo cheO P n (d) soddisfaN p ∀n≥p se e solo seO P p (d) satisfiesN p.相似文献