Journal of the Mathematical Society of Japan

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

Yoshihiro MIZUTA and Takao OHNO

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Abstract

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].

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 2 (2015), 433-452.

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1429624589

Digital Object Identifier
doi:10.2969/jmsj/06720433

Mathematical Reviews number (MathSciNet)
MR3340181

Zentralblatt MATH identifier
1298.31006

Subjects
Primary: 31B15: Potentials and capacities, extremal length 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
maximal functions Lorentz space of variable exponent Riesz potential Sobolev embeddings Sobolev's inequality

Citation

MIZUTA, Yoshihiro; OHNO, Takao. Sobolev's inequality for Riesz potentials in Lorentz spaces of variable exponent. J. Math. Soc. Japan 67 (2015), no. 2, 433--452. doi:10.2969/jmsj/06720433. https://projecteuclid.org/euclid.jmsj/1429624589


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References

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