共查询到20条相似文献,搜索用时 78 毫秒
1.
Ki-Ho Kwon 《Israel Journal of Mathematics》1994,86(1-3):409-427
Suppose thatα>1, 0<R<∞ and thatf is analytic in |z|≤αR with |f(0)|≥1. It is shown that for a constant dα depending only onα,
. Therefore iff is entire of order λ<∞, logM(r,f)/T(r,f) has order at most λ/2. These results are shown by example to be quite precise. 相似文献
2.
Evgeniy Pustylnik 《Journal d'Analyse Mathématique》1999,79(1):113-157
The Lorentz-Zygmund spaces, introduced by C. Bennett and K. Rudnick in [BR], are generalized by taking the exterior norm in
arbitrary rearrangement invariant spaceE instead of onlyL
r-spaces. On the spacesL
p,α,E thus obtained, we study all operatorsT of two weak types (a, b) and (p, q) with 1≤a<p≤∞, 1≤b<q≤∞, and prove thatT:L
p,α,E→L
q,α−1,E. Moreover, for any set of parametersp, q, α, E, we construct the smallest possible spaceB
q,α,E such thatT:L
p,α,E→B
q,α,E and the largest possible spaceA
p,α,E such thatT:A
p,α,E→L
q,α−1,E. For spaces of all three types, we find their fundamental functions and Boyd indices, state various embeddings, equivalences
and other properties.
The research was supported by the Center of Scientific Absorption of the Ministry of Absorption of the State of Israel. 相似文献
3.
Tamar Burak 《Israel Journal of Mathematics》1973,16(4):404-417
Fort ∈ [a, b], letA(t) be the unbounded operator inH
0,p
(G) associated with an elliptic-boundary value problem that satisfies Agmon’s conditions on the rays λ=±iτ, τ ≥0. Existence and uniqueness results are obtained for weak and strict solutions of two-point problems of the type (du/dt)−A(t) u(t) =f(t),E
1(α)u (α)=u
α,E
2 (β)u (β)=u
β. Here [α, β) χ- [a, b],E
1 (α) andE
2 (β) are spectral projections associated withA(α) andA(β) respectively, andA(α)E
1 (α) and =A (β)E
2 (β) are infinitesimal generators of analytic semigroups. WhenA(t) andf(t) are analytic in a convex, complex neighborhoodO of [a, b] we show that for someθ
i
,i=1,2, any solution ofdu/dt =A(t)u (t)=f(t) in [a, b] is analytic and satisfies the above equation in the setO∩{t; t ≠ a, t ≠ b, | arg (t −a) | <θ
1, | arg (b −t) |θ
2}.
Research partially supported by N. N. F. grant at Brandeis University. 相似文献
4.
E. P. Golubeva 《Journal of Mathematical Sciences》2007,143(3):3017-3022
Let p be a prime and let 1 ≤ a ≤ p − 1. In the paper, an asymptotics for the sum over a of the moments of order α (0 < α <
1) of the sequence of elements of the expansion of a/p into a continued fraction is obtained. As a corollary, an upper bound
for the number of those a whose expansions contain at least one element larger than log
λ p (λ > 1) is derived.
Note that in the case considered, the set of elements has no limiting distribution as p → ∞, which is in contrast with the
case of rational fractions b/c, where (b, c) = 1 and b2 + c2 ≤ R2 (R → ∞). Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 13–22. 相似文献
5.
Baode Li Yinsheng Jiang Hui Cao 《分析论及其应用》2007,23(2):138-146
In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator,simply CZO On Herz space and weak Herz space.In particular,we obtain vector-valued inequalities for CZO on Lq(Rd,│x│αdμ)space,with 1<q<∞,-n<α<n(q-1),and on L1,∞(Rd,│x│αdμ)space,with -n<α<0. 相似文献
6.
Yinsheng Jiang Lin Tang 《分析论及其应用》2005,21(4):301-310
In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKα,p q(G) and HKq,p q(G), where 1 < q <∞, Q(1 - 1/q) ≤α<∞, 0 < p <∞ and G denotes a graded homogeneous Lie group. 相似文献
7.
E. G. Goluzina 《Journal of Mathematical Sciences》1996,79(5):1304-1307
We study the structural properties of the class Mk,λ,b(k≥2, 0≤λ≤1, b∈ℂ\{0}) of functions f(z)=z+ ... which are regular in |z|<1 and satisfy the conditions f(z)f′(z)z−1≠0 and
, where J(z)=λ(1+b−1zf″(z)/f′(z)+(1−λ)(b−1zf′(z)/f(z)+1−b−1). The value regions of some functionals on this class are found. The case λ=1 was considered in our previous paper. Bibliography:
4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 55–60.
Translated by O. A. Ivanov. 相似文献
8.
On weighted approximation by Bernstein-Durrmeyer operators 总被引:6,自引:0,他引:6
Zhang Zhenqiu 《分析论及其应用》1991,7(2):51-64
In this paper, we consider weighted approximation by Bernstein-Durrmeyer operators in Lp[0, 1] (1≤p≤∞), where the weight function w(x)=xα(1−x)β,−1/p<α, β<1-1/p. We obtain the direct and converse theorems. As an important tool we use appropriate K-functionals.
Supported by Zhejiang Provincial Science Foundation. 相似文献
9.
The Besov spacesB
p
α,μ
(Γ) and Triebel-Lizorkin spacesF
p
α,μ
(Γ) with high order α∈R on a Lipschitz curve Γ are defined. when 1≤p≤∞, 1≤q≤∞. To compare to the classical case a difference
characterization of such spaces in the case |α|<1 is given also.
The author is supported in part by the Foundation of Zhongshan University Advanced Research Centre and NSF of China. 相似文献
10.
G. S. Pandey 《Annali di Matematica Pura ed Applicata》1964,64(1):109-122
Summary In the present paper the strong summability with index p/p−1
,1 < p < 2 of Jacobi series has been investigated. The result obtained includes as a particular case that of Foà (1943) and
Gupta (1959) for Legendre series. For α = β = λ − 1/2 it holds good for the ultraspherical series also. 相似文献
11.
Let A denote the class of functions which are analytic in |z|<1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A
be the class of functions f such thatRe[f′(z)+αzf″(z)]>β,Re α>0, β<1. We determine conditions under which (i) f ∈ R(α1, β1), g ∈ R(α2, β2) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β1), g ∈ R(0, β2) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]μ-1 ≺ 1 + λz, μ>0, 0<λ<1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α>0, δ>0, is convex or starlike. Bibliography:
16 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 138–154. 相似文献
12.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
13.
We study the zero-varieties of holomorphic functions in the unit ball satisfying the growth condition log |f(z)|≤c
fλ(|z|), where λ:(0,1)→ℝ+ is a positive increasing function. We obtain some sufficient conditions on an analytic variety to be defined by such a function.
Some results for the particular case λ(r)=log(e/(1−r)), corresponding to the classA
−∞, generalize those of B. Korenblum in one variable.
Both authors supported by DGICYT grant PB92-0804-C02-02. 相似文献
14.
Min Guohua 《分析论及其应用》1992,8(3):28-37
In this paper, the Lp-convergence of Grünwald interpolation Gn(f,x) based on the zeros of Jacobi polynomials J
n
(α,β)
(x)(−1<α,β<1) is considered. Lp-convergence (0<p<2) of Grünwald interpolation Gn(f,x) is proved for p·Max(α,β)<1. Moreover, Lp-convergence (p>0) of Gn(f,x) is obtained for −1<α,β≤0. Therefore, the results of [1] and [3–5] are improved. 相似文献
15.
S. V. Kerov 《Functional Analysis and Its Applications》2000,34(1):41-51
We study the Young lattice with the edge multiplicitiesϰ
α
(λ, ⋏) arising in the simplest Pieri formula for Jack symmetric polynomialsP
λ (x; α) with parameter α. A new proof of Stanley’s α-version of the hook formula is given. We also prove the formula
whereϕ(λ) = ∏
b∈λ
(a(b)α +l(b) + 1)−1 andc
α(b) is the α-contents of the new boxb=⋏/λ.
Partially supported by the Federal Grant Program “Integration,” No. 326.53, and by MSRI at Berkeley.
St. Petersburg Division of the V. A. Steklov Mathematical Institute. Translated from Funksional’nyi Analiz i Ego Prilozheniya,
Vol. 34, No. 1, pp. 51–64, January–March, 200.
Translated by S. V. Kerov 相似文献
16.
Ferenc Weisz 《分析论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded
from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H
1
#
(T×T), L1(T2)), where the Hardy space H
1
#
(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H
1
#
(T×T)⊃LlogL(T
2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces
Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.
This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt
Foundation. 相似文献
17.
Ferenc Weisz 《逼近论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. 相似文献
18.
V. M. Evtukhov 《Mathematical Notes》2000,67(2):160-167
For the nonlinear differential equation
whereσ>−1, λ<1, andp: [a, +∞[→]0, +∞[ is a continuous function, we establish sufficient criteria for the nonoscillation of all regular solutions;
in the case of the classical generalized Emden-Fowler equation (λ=0) these criteria supplement well-known results.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 201–210, February, 2000. 相似文献
19.
LetX be a Banach space and leta, b, q be real numbers such thata<b,q>0. Denote byD a locally closed subset ofX. A necessary and sufficient condition for the existence of a mild solutionu∈C([a−q, b
1],X),a<b
1<b, to the differential equationdu(t)/dt=Au(t)+f(t, u
t), such thatu:[a,b
1]→D, u
a=ϕ is given. The linear operatorA is the generator of aC
0 semigroupT(t), t≧0, withT(t) compact fort>0,f: [a, b)×C([−q,0],D
λ)→X is continuous and ϕ∈C([−q,0],D
λ) with ϕ(0)∈D. D
λ is a neighbourhood ofD. Applications to parabolic partial differential equations with retarded argument are given. 相似文献
20.
Bao Quan YUAN 《数学学报(英文版)》2008,24(2):253-266
The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^*,γ(R^n), with 1〈p〈∞and A = n-(2α-1)p, and for a small external force in a time-weighted weak Morrey space. 相似文献