Commutators of singular integrals on generalized $L^p$ spaces with variable exponent

By A. Karlovich, Andrei K. Lerner. 2004

63 citations recorded by the source corpus.

A classical theorem of Coifman, Rochberg, and Weiss on commutators of singular integrals is extended to the case of generalized $L^p$ spaces with variable exponent.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b0f8ef91cad6649bbe764be5f3f0a683ee39e60c

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In Applied Mathematics

1. D. Cruz-Uribe
2. S. Samko
3. C. P'erez
4. J. M. Martell
5. Andrei K. Lerner
6. Alberto Fiorenza
7. Mitsuo Izuki
8. V. Kokilashvili

In Mathematical Physics

1. D. Cruz-Uribe
2. S. Samko
3. V. Kokilashvili
4. Mitsuo Izuki
5. Alberto Fiorenza
6. J. M. Martell
7. C. P'erez
8. P. Hasto

Citations in the corpus

• Operators of harmonic analysis in weighted spaces with non-standard growth (2008, background): “the space Lp(·) (Rn). 21 In the case of constant p and ∈ Ap(Rn),1 < p < ∞, Theorem 4.25 was proved in [60]. In the case of variable p(·), the non-weighted case of Theorem 4.25 was proved in [30] under the assumption that 1 ∈ Ap(·)(R n). Corollary 4.26. Let the kernel K(x,y) fulfill conditions”
• THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES (2006, background): “Very recently, the boundedness of commutators on variable L spaces was proved by Karlovich and Lerner [27].”
• Boundedness of commutators on Herz spaces with variable exponent (2010, background): “the fundamental paper [9] by Kov´ay cik and R´ akosn´ ik. Recently Cruz-Uribe, Fiorenza, Martell and P´ erez [2] have proved the extrapolation theorem which leads the boundedness of some classical operators including the commutator on L p( ·) (R n ). Karlovich and Lerner [ 8 ] have also independentl”