Sobolev's inequality for Riesz potentials in Lorentz spaces of variable exponent

Yoshihiro Mizuta; Takao Ohno

doi:10.2969/jmsj/06720433

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Sobolev's inequality for Riesz potentials in Lorentz spaces of variable exponent

Yoshihiro Mizuta, Takao Ohno

著者情報

キーワード: maximal functions, Lorentz space of variable exponent, Riesz potential, Sobolev embeddings, Sobolev's inequality

ジャーナルフリー

2015 年 67 巻 2 号 p. 433-452

DOI https://doi.org/10.2969/jmsj/06720433

詳細

抄録

In the present paper we discuss the boundedness of the maximal operator in the Lorentz space of variable exponent defined by the symmetric decreasing rearrangement in the sense of Almut [1]. As an application of the boundedness of the maximal operator, we establish the Sobolev inequality by using Hedberg's trick in his paper [10].