Riv. Mat. Univ. Parma, Vol. 9, No. 1, 2018

Kwok-Pun Ho [a]

Mixed norm Lebesgue spaces with variable exponents and applications

Pages: 21-44
Accepted: 25 May 2018
Mathematics Subject Classification (2010): 42B35, 42B20, 46E30, 31C05.
Keywords: Mixed-norm spaces, Lebesgue spaces with variable exponent, extrapolation, product domains, Calderón-Zygmund operators, Littlewood-Paley operators, bi-harmonic functions, Ricci-Stein singular integrals, BMO.
[a]: The Education University of Hong Kong, 10 Lo Ping Road, Tai Po Hong Kong, China

Abstract: In this paper, we introduce the mixed norm Lebesgue spaces with variable exponent. We use this family of function spaces to study Calderón-Zygmund operators on product domains, the Littlewood-Paley operators associated with family of disjoint rectangles, the non-tangential maximal function and the area function for bi-harmonic functions, the Ricci-Stein singular integrals and the characterizations of the function space of bounded mean oscillation.

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