Journal of the Mathematical Society of Japan

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

Yoshihiro MIZUTA, Eiichi NAKAI, Yoshihiro SAWANO, and Tetsu SHIMOMURA

Full-text: Open access

Abstract

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 $\Phi(x,t)=t^{p(x)}(\log(c_0+t))^{q(x)}$ for $t$ > 0 and $x \in {\mathbb R}^n$, via the Littlewood-Paley decomposition.

Article information

Source
J. Math. Soc. Japan Volume 65, Number 2 (2013), 633-670.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1366896646

Digital Object Identifier
doi:10.2969/jmsj/06520633

Mathematical Reviews number (MathSciNet)
MR3055598

Zentralblatt MATH identifier
1269.31005

Subjects
Primary: 31B15: Potentials and capacities, extremal length 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
Gagliardo-Nirenberg inequality Riesz potentials variable exponents Musielak-Orlicz spaces Littlewood-Paley theory

Citation

MIZUTA, Yoshihiro; NAKAI, Eiichi; SAWANO, Yoshihiro; SHIMOMURA, Tetsu. Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials. J. Math. Soc. Japan 65 (2013), no. 2, 633--670. doi:10.2969/jmsj/06520633. https://projecteuclid.org/euclid.jmsj/1366896646.


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