Littlewood–Paley characterizations of Triebel–Lizorkin–Morrey spaces via ball averages. (February 2017)

• Record Type: Journal Article
• Authors: Zhang, Junwei; Zhuo, Ciqiang; Yang, Dachun; He, Ziyi
• Is Part Of: Nonlinear analysis. Volume 150(2017)
• Page Start: 76
• Page End: 103
• Publication Date: 2017-02
• Subjects: primary 46E35 -- secondary 42B25 42B35; Triebel–Lizorkin–Morrey space -- Littlewood–Paley function -- Ball average; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.11.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let 1 < p ≤ u < ∞ and q ∈ ( 1, ∞ ] . In this article, the authors establish equivalent characterizations of the Triebel–Lizorkin–Morrey space E u, q, p α ( R n ) with smoothness order α ∈ ( 0, 2 ) in terms of the Lusin-area function and the g λ ∗ -function generated by the difference between f ( x ) and its ball average B 2 − j f ( x ) : = 1 | B ( x, 2 − j ) | ∫ B ( x, 2 − j ) f ( y ) d y, ∀ j ∈ { 1, 2, … }, ∀ x ∈ R n, where, for any j ∈ { 1, 2, … } and x ∈ R n, B ( x, 2 − j ) : = { y ∈ R n : | y − x | < 2 − j } . As applications, the authors obtain several characterizations of E u, ∞, p α ( R n ) via pointwise inequalities involving ball averages.