Displaying similar documents to “Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces.”

On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Ali Akbulut, Vagif Guliyev, Rza Mustafayev (2012)

Mathematica Bohemica

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In the paper we find conditions on the pair ( ω 1 , ω 2 ) which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space ℳ p , ω 1 to another ℳ p , ω 2 , 1 < p < ∞ , and from the space ℳ 1 , ω 1 to the weak space W ℳ 1 , ω 2 . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.

The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces

Rovshan A. Bandaliev (2010)

Czechoslovak Mathematical Journal

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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.

Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu, Yue Ping Zhu (2014)

Czechoslovak Mathematical Journal

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We introduce a new type of variable exponent function spaces M K ˙ q , p ( · ) α ( · ) , λ ( ℝ n ) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators...

Corrections to the paper “The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces“

Rovshan A. Bandaliev (2013)

Czechoslovak Mathematical Journal

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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...