The Ahlfors–Beurling transform on Morrey spaces with variable exponents. Issue 3 (4th March 2018)

• Record Type: Journal Article
• Authors: Ho, Kwok-Pun
• Is Part Of: Integral transforms and special functions. Volume 29:Issue 3(2018)
• Page Start: 207
• Page End: 220
• Publication Date: 2018-03-04
• Subjects: Ahlfors–Beurling transform -- Morrey space -- Lebesgue space -- variable exponent; 42B20 -- 42B35 -- 46E30; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2017.1422498
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: We establish the vector-valued inequalities of the Ahlfors–Beurling operator on Morrey spaces with variable exponents. As consequences of these inequalities, we have the boundedness of the Ahlfors–Beurling transform on Lebesgue spaces with variable exponents and Morrey spaces. The results obtained in this paper are new in the case of Morrey spaces.