Mixed norm Lebesgue spaces with variable exponents and applications
Received: 23 October 2017
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 LittlewoodPaley operators associated with family of disjoint rectangles, the nontangential 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.