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http://dx.doi.org/10.4134/BKMS.b170212

A NOTE OF LITTLEWOOD-PALEY FUNCTIONS ON TRIEBEL-LIZORKIN SPACES  

Liu, Feng (College of Mathematics and Systems Science Shandong University of Science and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 659-672 More about this Journal
Abstract
In this note we prove that several classes of Littlewood-Paley square operators defined by the kernels without any regularity are bounded on Triebel-Lizorkin spaces $F^{p,q}_{\alpha}({\mathbb{R}}^n)$ and Besov spaces $B^{p,q}_{\alpha}({\mathbb{R}}^n)$ for 0 < ${\alpha}$ < 1 and 1 < p, q < ${\infty}$.
Keywords
Littlewood-Paley function; Triebel-Lizorkin spaces; Besov spaces; extrapolation;
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