Futamura, Toshihide; Mizuta, Yoshihiro; Ohno, Takao Sobolev’s theorem for Riesz potentials of functions in grand Morrey spaces of variable exponent. (English) Zbl 1332.31007 Kato, Mikio (ed.) et al., Proceedings of the 4th international symposium on Banach and function spaces IV (ISBFS 2012), Kitakyushu, Japan, September 12–15, 2012. Yokohama: Yokohama Publishers (ISBN 978-4-946552-48-9/hbk). 353-365 (2014). Summary: In this paper we first study the boundedness of the maximal operator in grand Morrey spaces of variable eponent. As an application of the boundedness of maximal operator, we give Sobolev’s inequality for Riesz potentials of functions in grand Morrey spaces of variable exponent, as an extension of [A. Meskhi, Complex Var. Elliptic Equ. 56, No. 10–11, 1003–1019 (2011; Zbl 1261.42022)]. Further we are concerned with Trudinger’s type exponential integrability and the continuity for Riesz potentials.For the entire collection see [Zbl 1297.46002]. Cited in 6 Documents MSC: 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:maximal function; Sobolev’s inequality; Trudinger’s inequality Citations:Zbl 1261.42022 PDFBibTeX XMLCite \textit{T. Futamura} et al., in: Proceedings of the 4th international symposium on Banach and function spaces IV (ISBFS 2012), Kitakyushu, Japan, September 12--15, 2012. Yokohama: Yokohama Publishers. 353--365 (2014; Zbl 1332.31007)