Sobolev‐type inequalities for potentials in grand variable exponent Lebesgue spaces
Copyright policy )Sobolev‐type inequalities for potentials in grand variable exponent Lebesgue spaces
AbstractWe introduce a new scale of grand variable exponent Lebesgue spaces denoted by . These spaces unify two non‐standard classes of function spaces, namely, grand Lebesgue and variable exponent Lebesgue spaces. The boundedness of integral operators of Harmonic Analysis such as maximal, potential, Calderón–Zygmund operators and their commutators are established in these spaces. Among others, we prove Sobolev‐type theorems for fractional integrals in . The spaces and operators are defined, generally speaking, on quasi‐metric measure spaces with doubling measure. The results are new even for Euclidean spaces.
- International Black Sea University Georgia
- Georgian Technical University Georgia
- University of Sussex United Kingdom
- Tbilisi State University Georgia
Lebesgue spaces, commutators, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, Sobolev inequality, Calderón-Zygmund operators, grand spaces, variable exponents, maximal operator, potential operators, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Lebesgue spaces, commutators, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, Sobolev inequality, Calderón-Zygmund operators, grand spaces, variable exponents, maximal operator, potential operators, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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