Journal Article10.2996/KMJ/1490083222
Herz-type Besov spaces of variable smoothness and integrability
Douadi Drihem,Rabah Heraiz +1 more
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TL;DR: In this paper, Herz-type Besov spaces with variable smoothness and integrability are introduced, and they are proved to have the same properties as Sobolev-type embeddings.
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Abstract: In this paper, Herz-type Besov spaces with variable smoothness and integrability are introduced. Our scale contains variable Besov spaces as special cases. We prove several basic properties, especially the Sobolev-type embeddings.
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Citations
Estimates of bilinear pseudodifferential operators associated to bilinear Hörmander classes in Besov and Triebel-Lizorkin spaces with variable exponents.
Jingshi Xu,Jinlai Zhu +1 more
TL;DR: Leibniz-type estimates of bilinear pseudodifferential operators associated to bil inear Hörmander classes in Besov and Triebel–Lizorkin spaces with variable exponents are given.
Variable Herz Estimates for Fractional Integral Operators
TL;DR: In this paper, the problem of boundedness of fractional integral operators on a variable Herz-type Hardy space was studied and the atomic decomposition was used to prove the boundedness.
1
•Journal Article
On the Boundedness of Marcinkiewicz Integrals on Variable Exponent Herz-type Hardy Spaces
TL;DR: In this article, it was shown that α(·, p·) and q(·) satisfies some conditions, and the boundedness of μ on variable Herz-type Hardy spaces was proved.
Mixed-norm Herz spaces and their applications in related Hardy spaces
TL;DR: In this paper , the authors introduced a class of mixed-norm Herz spaces, which is a natural generalization of mixednorm Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed norm Lebesge spaces, and gave their dual spaces and obtained the Riesz-Thorin interpolation theorem on [Formula: see text].
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