Papers by Alexander Meskhi
Banach Journal of Mathematical Analysis, Jan 31, 2020
Journal of Inequalities and Applications, 2008
A measure of noncompactness essential norm for maximal functions and potential operators defined ... more A measure of noncompactness essential norm for maximal functions and potential operators defined on homogeneous groups is estimated in terms of weights. Similar problem for partial sums of the Fourier series is studied. In some cases, we conclude that there is no weight pair for which these operators acting between two weighted Lebesgue spaces are compact.
Journal of Mathematical Sciences, Nov 24, 2022
Canadian Journal of Mathematics, Jun 1, 2000
Two-weight inequalities of strong and weak type are obtained in the context of spaces of homogene... more Two-weight inequalities of strong and weak type are obtained in the context of spaces of homogeneous type. Various applications are given, in particular to Cauchy singular integrals on regular curves.
arXiv (Cornell University), Apr 10, 2012
Journal of Mathematical Sciences
arXiv (Cornell University), Jul 8, 2010
In the paper two-weighted norm estimates with general weights for Hardy-type transforms, maximal ... more In the paper two-weighted norm estimates with general weights for Hardy-type transforms, maximal functions, potentials and Calderón-Zygmund singular integrals in variable exponent Lebesgue spaces defined on quasimetric measure spaces (X, d, µ) are established. In particular, we derive integral-type easily verifiable sufficient conditions governing two-weight inequalities for these operators. If exponents of Lebesgue spaces are constants, then most of the derived conditions are simultaneously necessary and sufficient for appropriate inequalities. Examples of weights governing the boundedness of maximal, potential and singular operators in weighted variable exponent Lebesgue spaces are given.
arXiv (Cornell University), Jul 7, 2010
It is shown that that the fractional integral operators with the parameter α, 0 < α < 1, are not ... more It is shown that that the fractional integral operators with the parameter α, 0 < α < 1, are not bounded between the generalized grand Lebesgue spaces L p),θ 1 and L q),θ 2 for θ 2 < (1 + αq)θ 1 , where 1 < p < 1/α and q = p 1-αp . Besides this, it is proved that the one-weight inequality where I α is the Riesz potential operator on the interval [0, 1], holds if and only if w ∈ A 1+q/p ′ .
Banach Journal of Mathematical Analysis, 2020
Journal of the Korean Mathematical Society, 2009
Spectral Theory, Function Spaces and Inequalities, 2011
Zeitschrift für Analysis und ihre Anwendungen, 2005
Approximation and Probability, 2006
Georgian Mathematical Journal - GEORGIAN MATH J, 1999
The optimal sufficient conditions are found for weights, which guarantee the validity of two-weig... more The optimal sufficient conditions are found for weights, which guarantee the validity of two-weighted inequalities for singular integrals in the Lorentz spaces defined on homogeneous groups. In some particular case, the found conditions are necessary for the corresponding inequalities to be valid. Also, the necessary and sufficient conditions are found for pairs of weights, which provide the validity of two-weighted inequalities for the generalized Hardy operator in the Lorentz spaces defined on homogeneous groups.
Journal of Inequalities and Applications, 2010
Journal of Inequalities and Applications, 2008
Georgian Mathematical Journal, 2013
Houston journal of …, 2009
Journal of Functional Analysis, 2010
The relationship between the operator norms of fractional integral operators acting on weighted L... more The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.
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Papers by Alexander Meskhi