scholarly journals Extrapolation to mixed norm spaces and applications

2021 ◽  
Vol 25 (2) ◽  
pp. 281-296
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Lorentz Spaces ◽  
Maximal Functions ◽  
Mixed Norm ◽  
Variable Exponents ◽  
Lebesgue Spaces ◽  
Mixed Norm Spaces ◽  
Special Cases ◽  
Extrapolation Theory

This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.

scholarly journals Some mixed paranorm spaces

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1079-1098 ◽  
Author(s):  
Eberhard Malkowsky ◽  
Faruk Özger ◽  
Vesna Velickovic
Keyword(s):  
Mixed Norm ◽  
Topological Properties ◽  
Mixed Norm Spaces ◽  
Special Cases

We generalize the concept of mixed norm spaces and define a class of mixed paranorm spaces, study their fundamental topological properties and determine their first and second duals. Furthermore we obtain the corresponding known results for mixed norm spaces and spaces of sequences that are strongly summable to zero as special cases of our new results.

scholarly journals Matrix transformations on mixed paranorm spaces

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2957-2966 ◽  
Author(s):  
Eberhard Malkowsky ◽  
Faruk Özger ◽  
Vesna Velickovic
Keyword(s):  
Convergent Series ◽  
Mixed Norm ◽  
Matrix Transformations ◽  
Mixed Norm Spaces ◽  
Special Cases

Recently the concept of mixed norm spaces was generalized to that of the mixed paranorm spaces [l(r),lp]<k(v)>. Here we determine the classes of matrix transformations from [l(r),lp]<k(v)> into the spaces of bounded, convergent and null sequences, and into the spaces of all bounded, convergent and absolutely convergent series. We also obtain many correponding known results for mixed norm spaces as special cases and visualize some neighborhoods in the spaces [l(r),lp]<k(v)>.

scholarly journals Fourier multipliers on anisotropic mixed-norm spaces of distributions

2019 ◽  
Vol 124 (2) ◽  
pp. 289-304 ◽  
Author(s):  
Galatia Cleanthous ◽  
Athanasios G. Georgiadis ◽  
Morten Nielsen
Keyword(s):  
Fourier Multipliers ◽  
Mixed Norm ◽  
Type Condition ◽  
Lebesgue Spaces ◽  
Mixed Norms ◽  
Mixed Norm Spaces ◽  
Equivalent Norms

A new general Hörmander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multipliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operators is established on mixed Sobolev and Lebesgue spaces too. Some lifting properties and equivalent norms are obtained as well.

scholarly journals Calderón Operator on Local Morrey Spaces with Variable Exponents

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2977
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Hölder Continuity ◽  
Morrey Spaces ◽  
Variable Exponents ◽  
Holder Continuity ◽  
Averaging Operators ◽  
Special Cases ◽  
Continuity Assumption ◽  
Hardy’S Inequalities ◽  
Extrapolation Theory ◽  
Local Morrey Spaces

In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents.

Adjoint of generalized Cesáro operators on analytic function spaces

2020 ◽  
Vol 26 (2) ◽  
pp. 185-192
Author(s):  
Sunanda Naik ◽  
Pankaj K. Nath
Keyword(s):  
Analytic Function ◽  
Convolution Operator ◽  
Composition Operators ◽  
Mixed Norm ◽  
Averaging Operators ◽  
Mixed Norm Spaces ◽  
Cesaro Averaging ◽  
Analytic Function Spaces ◽  
Appl Math ◽  
Two Parameter

AbstractIn this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 2009, 2, 304–311]. Also we consider the adjoint {\mathcal{A}^{b,c}} for {b>0} of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces {B_{\alpha+(c-1)}^{p,q}} for {c>1}.

Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces

2020 ◽  
Vol 23 (5) ◽  
pp. 1452-1471
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Riesz Potential ◽  
Fractional Integrals ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient ◽  
Bounded Sets ◽  
Trace Inequalities

Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

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