Continuity of pseudodifferential operators on mixed-norm Lebesgue spaces

2019 ◽  
Vol 190 (4) ◽  
pp. 657-674
Author(s):  
Nenad Antonić ◽  
Ivan Ivec ◽  
Ivana Vojnović
Keyword(s):  
Pseudodifferential Operators ◽  
Mixed Norm ◽  
Lebesgue Spaces

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.

scholarly journals New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces \({L_{\vec{p}}(\mathbb{R}^d)}\)

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 227 ◽  
Author(s):  
Junjian Zhao ◽  
Wei-Shih Du ◽  
Yasong Chen
Keyword(s):  
Invariant Subspace ◽  
Type Inequality ◽  
Invariant Subspaces ◽  
Minkowski Inequality ◽  
Hölder Inequality ◽  
Stability Theorem ◽  
Mixed Norm ◽  
Lebesgue Spaces

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of Lp→(Rd). Our new results unify and refine the existing results in the literature.

scholarly journals Compactness of integral operators in Lebesgue spaces with mixed norm

2008 ◽  
pp. 335-348
Author(s):  
Alberto Fiorenza ◽  
Babita Gupta ◽  
Pankaj Jain
Keyword(s):  
Integral Operators ◽  
Mixed Norm ◽  
Lebesgue Spaces

On Hardy Inequality in Variable Lebesgue Spaces with Mixed Norm

2018 ◽  
Vol 49 (4) ◽  
pp. 765-782 ◽  
Author(s):  
Rovshan A. Bandaliyev ◽  
Ayhan Serbetci ◽  
Sabir G. Hasanov
Keyword(s):  
Hardy Inequality ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces
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