Multiple weight Riesz and Fourier transforms in bilateral anisotropic Grand Lebesgue spaces

2012/08/12 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1 · 5 citations
Mathematics · #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1208.2392

openalex publication_date 2012/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short article we introduce so-called anisotropic (weight) Grand Lebesgue Spaces (more exactly, Grand Lebesgue-Riesz Spaces), which are generalization of the classical Lebesgue-Riesz Spaces and ordinary Grand Lebesgue Spaces, and investigate the boundedness of weight Riesz potential and weight Fourier transforms in this spaces.

Citations

• Nikol'skii-type inequalities for rearrangement invariant spaces
• Integral Operators in Bilateral Grand Lebesgue Spaces

Cited by

• Sharp estimates for module of continuity of fractional integrals and derivatives
• Lebesgue spaces norm estimates for fractional integrals and derivatives
• Lebesgue-Riesz norm estimates for fractional Laplace transform
• Mixed Lebesgue space norm Strichartz type estimation for solution of inhomogeneous parabolic equation, with constants evaluation
• Cesaro-Hardy operators on bilateral grand Lebesgue spaces

Related

• Riesz's and Bessel's Operators in Bilateral Grand Lebesgue Spaces
• Fourier Series and Transforms in Grand Lebesgue Spaces As an particular case - exponential Orlicz spaces
• Boundedness of Operators in Bilateral Grand Bebesgue Spaces with Exact\n and Weakly Exact Constant Calculation
• Anisotropic Grand Lorentz Spaces
• A Two-Weight Boundedness Criterion and Its Applications