Operators of harmonic analysis in weighted spaces with non-standard growth

By V. Kokilashvili, S. Samko. 2008

68 citations recorded by the source corpus.

Last years there was increasing an interest to the so-called function spaces with non-standard growth, known also as variable exponent Lebesgue spaces. For weighted such spaces on homogeneous spaces, we develop a certain variant of Rubio de Francia's extrapolation theorem. This extrapolation theorem is applied to obtain the boundedness in such spaces of various operators of harmonic analysis, such as maximal and singular operators, potential operators, Fourier multipliers, dominants of partial sums of trigonometric Fourier series and others, in weighted Lebesgue spaces with variable exponent. There are also given their vector-valued analogues.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/5db6acb581e5f60826198d7509c8fda8cf440869

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In Applied Mathematics

1. Yoshihiro Sawano
2. S. Samko
3. E. Nakai
4. Mitsuo Izuki
5. Vagif S. Guliyev
6. J. Hasanov
7. Dachun Yang
8. Kwok-Pun Ho

Citations in the corpus

• Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces (2010, background): “Such inequalities are also of interest when they allow to impose different conditions as r → 0 and r → ∞; such a case was dealt with in [35], [23].”
• FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, methodology): “For example, the former is used in [200], and, the latter is used in [90, 91, 98].”