Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials

Yoshihiro Mizuta; Eiichi Nakai; Yoshihiro Sawano; Tetsu Shimomura

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Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials

机译：可变指数Lebesgue空间的Littlewood-Paley理论和Riesz势的Gagliardo-Nirenberg不等式

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摘要

Our aim in this paper is to prove the Gagliardo-Nirenberg inequality for Riesz potentials of functions in variable exponent Lebesgue spaces, which are called Musielak-Orlicz spaces with respect to Φ(x, t) = t~P(x)(log(c_0 + t)) ~q(x) for t > 0 and x ∈ R~n, via the Littlewood-Paley decomposition.

机译：本文的目的是证明变量指数Lebesgue空间中函数的Riesz势的Gagliardo-Nirenberg不等式，相对于Φ（x，t）= t〜P（x）（log（通过Littlewood-Paley分解，对于t> 0和x∈R〜n时c_0 + t））〜q（x）。

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《Journal of the Mathematical Society of Japan》 |2013年第2期|633-670|共38页
作者
Yoshihiro Mizuta; Eiichi Nakai; Yoshihiro Sawano; Tetsu Shimomura;
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作者单位

Department of Mathematics Graduate School of Science Hiroshima University Higashi-Hiroshima 739-8521, Japan,Department of Mechanical Systems Engineering Hiroshima Institute of Technology 2-1-1 Miyake Saeki-ku Hiroshima 731-5193, Japan;

Department of Mathematics Kyoto University Kyoto, 606-8502, Japan,Department of Mathematics Ibaraki University Mito, Ibaraki 310-8512, Japan;

Department of Mathematics and Information Science Tokyo Metropolitan University 1-1 minami-Ohsawa, Hachioji Tokyo 192-0397, Japan;

Department of Mathematics Osaka Kyoiku University Kashiwara, Osaka 582-8582, Japan,Department of Mathematics Graduate School of Education Hiroshima University Higashi-Hiroshima 739-8524, Japan;

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收录信息美国《科学引文索引》(SCI);
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正文语种 eng
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2. Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces [J] . Almeida A., Harjulehto P., Hasto P., Annali di matematica pura ed applicata . 2015,第2期

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3. Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces [J] . Yoshihiro Sawano, Tetsu Shimomura Journal of inequalities and applications . 2013,第1期

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Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials

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