共查询到20条相似文献,搜索用时 46 毫秒
1.
David E. EDMUNDS Alberto FIORENZA Alexander MESKHI 《数学学报(英文版)》2006,22(6):1847-1862
The measure of non-compactness is estimated from below for various operators, including the Hardy-Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Lebesgue spaces. The identity operator acting between weighted Lebesgue spaces and also between the counterparts of these spaces with variable exponents is similarly analysed. These results enable the lack of compactness of such operators to be quantified. 相似文献
2.
Long Huang & Dachun Yang 《数学研究》2021,54(3):262-336
The targets of this article are threefold. The first one is to give a survey on the
recent developments of function spaces with mixed norms, including mixed Lebesgue
spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed
Morrey spaces as well as anisotropic mixed-norm Hardy spaces. The second one is
to provide a detailed proof for a useful inequality about mixed Lebesgue norms and
the Hardy–Littlewood maximal operator and also to improve some known results on
the maximal function characterizations of anisotropic mixed-norm Hardy spaces and
the boundedness of Calderón–Zygmund operators from these anisotropic mixed-norm Hardy spaces to themselves or to mixed Lebesgue spaces. The last one is to correct
some errors and seal some gaps existing in the known articles. 相似文献
3.
In this paper a two-weight boundedness of multidimensional Hardy operator and its dual operator acting from one weighted variable Lebesgue spaces with mixed norm into other weighted variable Lebesgue spaces with mixed norm spaces is proved. In particular, a new type two-weight criterion for multidimensional Hardy operator is obtained. 相似文献
4.
Rovshan A. Bandaliev 《Czechoslovak Mathematical Journal》2013,63(4):1149-1152
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in my paper, which was published as R.A.Bandaliev, The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces, Czech. Math. J. 60 (2010), 327–337. 相似文献
5.
S. M. Umarkhadzhiev 《Russian Mathematics (Iz VUZ)》2014,58(4):35-43
We introduce families of weighted grand Lebesgue spaces which generalize weighted grand Lebesgue spaces (known also as Iwaniec-Sbordone spaces). The generalization admits a possibility of expanding usual (weighted) Lebesgue spaces to grand spaces by various ways by means of additional functional parameter. For such generalized grand spaces we prove a theorem on the boundedness of linear operators under the information of their boundedness in ordinary weighted Lebesgue spaces. By means of this theorem we prove boundedness of the Hardy-Littlewood maximal operator and the Calderon-Zygmund singular operators in the weighted grand spaces. 相似文献
6.
The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents. 相似文献
7.
In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces L~p(R~n), Hardy spaces H~p(R~n) and general mixed norm spaces, which implies almost everywhere convergence of such operator. In this paper, we study the rate of convergence on fractional power dissipative operator on some sobolev type spaces. 相似文献
8.
Kwok-Pun Ho 《Integral Transforms and Special Functions》2018,29(3):207-220
We establish the vector-valued inequalities of the Ahlfors–Beurling operator on Morrey spaces with variable exponents. As consequences of these inequalities, we have the boundedness of the Ahlfors–Beurling transform on Lebesgue spaces with variable exponents and Morrey spaces. The results obtained in this paper are new in the case of Morrey spaces. 相似文献
9.
《Indagationes Mathematicae》2017,28(2):516-526
In this paper we introduce the weighted version of fully measurable grand Lebesgue spaces and obtain characterizations for the boundedness of maximal operator, Hilbert transform and the Hardy averaging operator on these spaces. 相似文献
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12.
Yi Huang 《Archiv der Mathematik》2018,111(6):633-646
In this article we generalize the singular integral operator theory on weighted tent spaces to spaces of homogeneous type. This generalization of operator theory is in the spirit of C. Fefferman and Stein since we use some auxiliary functionals on tent spaces which play roles similar to the Fefferman–Stein sharp and box maximal functions in the Lebesgue space setting. Our contribution in this operator theory is twofold: for singular integral operators (including maximal regularity operators) on tent spaces pointwise Carleson type estimates are proved and this recovers known results; on the underlying space no extra geometrical conditions are needed and this could be useful for future applications to parabolic problems in rough settings. 相似文献
13.
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
14.
Rovshan A. Bandaliev 《Czechoslovak Mathematical Journal》2010,60(2):327-337
The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue
spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted
variable Lebesgue space. 相似文献
15.
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of
certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces.
We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal
operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces. 相似文献
16.
We introduce the p-adic weighted multilinear Hardy-Cesàro operator. We also obtain the necessary and sufficient conditions on weight functions to ensure the boundedness of that operator on the product of Lebesgue spaces, Morrey spaces, and central bounded mean oscillation spaces. In each case, we obtain the corresponding operator norms. We also characterize the good weights for the boundedness of the commutator of weighted multilinear Hardy-Cesàro operator on the product of central Morrey spaces with symbols in central bounded mean oscillation spaces. 相似文献
17.
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
18.
Sufficient conditions on the kernel and the grandizer that ensure the boundedness of integral operators with homogeneous kernels in grand Lebesgue spaces on ? n as well as an upper bound for their norms are obtained. For some classes of grandizers, necessary conditions and lower bounds for the norm of these operators are also obtained. In the case of a radial kernel, stronger estimates are established in terms of one-dimensional grand norms of spherical means of the function. A sufficient condition for the boundedness of the operator with homogeneous kernel in classical Lebesgue spaces with arbitrary radial weight is obtained. As an application, boundedness in grand spaces of the one-dimensional operator of fractional Riemann–Liouville integration and of a multidimensional Hilbert-type operator is studied. 相似文献
19.
In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-H¨older continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces. 相似文献
20.
Amjad Hussain Naqash Sarfraz 《P-Adic Numbers, Ultrametric Analysis, and Applications》2020,12(1):29-38
The present article investigates the weak boundedness of fractional p-adic Hardy operators and their adjoints on Lebesgue spaces. It also furnishes the corresponding operator norms for such operators on these spaces. 相似文献