Taiwanese Journal of Mathematics

EXPONENTIAL INTEGRABILITY FOR LOGARITHMIC POTENTIALS OF FUNCTIONS IN GENERALIZED LEBESGUE SPACES $L(\log L)^{q(\cdot)}$ OVER NON-DOUBLING MEASURE SPACES

Sachihiro Kanemori, Takao Ohno, and Tetsu Shimomura

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Abstract

In this paper, we are concerned with exponential integrability for logarithmic potentials of functions in generalized Lebesgue spaces $L(\log L)^{q(\cdot)}$ over non-doubling measure spaces. Here $q$ satisfies the loglog-Hölder condition.

Article information

Source
Taiwanese J. Math., Volume 19, Number 6 (2015), 1795-1803.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133740

Digital Object Identifier
doi:10.11650/tjm.19.2015.5564

Mathematical Reviews number (MathSciNet)
MR3434278

Zentralblatt MATH identifier
1357.31006

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
exponential integrability logarithmic potential variable exponent metric measure space non-doubling measure

Citation

Kanemori, Sachihiro; Ohno, Takao; Shimomura, Tetsu. EXPONENTIAL INTEGRABILITY FOR LOGARITHMIC POTENTIALS OF FUNCTIONS IN GENERALIZED LEBESGUE SPACES $L(\log L)^{q(\cdot)}$ OVER NON-DOUBLING MEASURE SPACES. Taiwanese J. Math. 19 (2015), no. 6, 1795--1803. doi:10.11650/tjm.19.2015.5564. https://projecteuclid.org/euclid.twjm/1499133740


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