共查询到20条相似文献,搜索用时 15 毫秒
1.
K. Kazarian V. N. Temlyakov 《Proceedings of the Steklov Institute of Mathematics》2013,280(1):181-190
We consider a weighted L p space L p (w) with a weight function w. It is known that the Haar system H p normalized in L p is a greedy basis of L p , 1 < p < ∞. We study a question of when the Haar system H p w normalized in L p (w) is a greedy basis of L p (w), 1 < p < ∞. We prove that if w is such that H p w is a Schauder basis of L p (w), then H p w is also a greedy basis of L p (w), 1 < p < ∞. Moreover, we prove that a subsystem of the Haar system obtained by discarding finitely many elements from it is a Schauder basis in a weighted norm space L p (w); then it is a greedy basis. 相似文献
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Przemysław Górka 《Periodica Mathematica Hungarica》2016,72(2):243-247
We prove an Ergodic Theorem in variable exponent Lebesgue spaces, whenever the exponent is invariant under the transformation. Moreover, a counterexample is provided which shows that the norm convergence fails to hold for an arbitrary exponent. 相似文献
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We consider generalized potential operators with the kernel on bounded quasimetric measure space (X, μ, d) with doubling measure μ satisfying the upper growth condition μB(x, r) ? KrN, N ∈ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity we prove that such potential operators are bounded from the variable exponent Lebesgue space Lp(?)(X, μ) into a certain Musielak‐Orlicz space Lp(X, μ) with the N‐function Φ(x, r) defined by the exponent p(x) and the function a(r). A reformulation of the obtained result in terms of the Matuszewska‐Orlicz indices of the function a(r) is also given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
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Petteri Harjulehto Peter H?st? Yoshihiro Mizuta Tetsu Shimomura 《manuscripta mathematica》2011,135(3-4):381-399
In this paper we study the iterated Hardy?CLittlewood maximal operator in variable exponent Lebesgue spaces with exponent allowed to reach the value 1. We use modulars where the L p(·)-modular is perturbed by a logarithmic-type function, and the results hold also in the more general context of such Musielak?COrlicz spaces. 相似文献
5.
Tengiz Kopaliani 《Journal of Functional Analysis》2009,257(11):3541-3551
When Hardy-Littlewood maximal operator is bounded on Lp(⋅)(Rn) space we prove θ[Lp(⋅)(Rn),BMO(Rn)]=Lq(⋅)(Rn) where q(⋅)=p(⋅)/(1−θ) and θ[Lp(⋅)(Rn),H1(Rn)]=Lq(⋅)(Rn) where 1/q(⋅)=θ+(1−θ)/p(⋅). 相似文献
6.
《Mathematische Nachrichten》2017,290(2-3):187-200
In this paper we consider the k‐plane Nikodym maximal estimates in the variable Lebesgue spaces . We first formulate the problem about the boundedness of the k‐plane Nikodym maximal and show that the maximal estimate in is equivalent to that in for . So, the optimal Nikodym maximal estimate in follows from Cordoba's estimate. 相似文献
7.
N.G. Samko S.G. Samko B.G. Vakulov 《Journal of Mathematical Analysis and Applications》2007,335(1):560-583
For the Riesz potential operator Iα there are proved weighted estimates
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We apply the techniques of monotone and relative rearrangements to the nonrearrangement invariant spaces Lp()(Ω) with variable exponent. In particular, we show that the maps uLp()(Ω)→k(t)u*Lp*()(0,measΩ) and uLp()(Ω)→u*Lp*()(0,measΩ) are locally -Hölderian (u* (resp. p*) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents. 相似文献
10.
For and variable exponents and with values in [1, ∞], let the variable exponents be defined by The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space to the variable Lebesgue space for , then where C is an interpolation constant independent of T. We consider two different modulars and generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that and , as well as, lead to sufficient conditions for and . We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that , are Lipschitz continuous and bounded away from one and infinity (in this case, ). 相似文献
11.
Tengiz Kopaliani George Chelidze 《Journal of Mathematical Analysis and Applications》2009,356(1):232-817
We prove analogies of the classical Gagliardo-Nirenberg inequalities
12.
Analysis Mathematica - We give sufficient conditions on the exponent p: ℝd → [1, ∞) for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue spaces... 相似文献
13.
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered. 相似文献
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In this paper we prove that p-adic wavelets form an unconditional basis in the space L r (? p n ) and give the characterization of the space L r (? p n ) in terms of Fourier coefficients of p-adic wavelets.Moreover, the Greedy bases in the Lebesgue spaces on the field of p-adic numbers are also established. 相似文献
17.
Alexandre Almeida Humberto Rafeiro 《Journal of Mathematical Analysis and Applications》2008,340(2):1336-1346
We study the inversion problem of the Bessel potential operator within the frameworks of the weighted Lebesgue spaces with variable exponent. The inverse operator is constructed by using approximative inverse operators. This generalizes some classical results to the variable exponent setting. 相似文献
18.
Sadulla Z. Jafarov 《复变函数与椭圆型方程》2018,63(10):1444-1458
In the present work, we investigate the approximation problems of the functions by Fejér, and Zygmund means of Fourier trigonometric series in weighted Lebesgue spaces with variable exponents and of the functions by Fejér and Abel–Poisson sums of Faber series in weighted Smirnov classes with variable exponents defined on simply connected domains with a Dini-smooth boundary of the complex plane. 相似文献
19.
R. Akgün 《Ukrainian Mathematical Journal》2011,63(1):1-26
We investigate the approximation properties of the trigonometric system in L2pp( ·) L_{2pi }^{pleft( cdot right)} . We consider the moduli of smoothness of fractional order and obtain direct and inverse approximation theorems together with a constructive characterization of a Lipschitz-type class. 相似文献
20.
R. A. Bandaliev 《Lithuanian Mathematical Journal》2010,50(3):249-259
The main purpose of this paper is to prove a two-weight criterion for the multidimensional Hardy-type operator in weighted Lebesgue spaces with variable exponent. As an application, we prove the boundedness of Riesz potential and fractional maximal operators on the weighted variable Lebesgue space. 相似文献