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3 results

Trudinger’s inequalities for Riesz potentials in Morrey spaces of double phase functionals on half spaces
Part of
Yoshihiro Mizuta, Tetsu Shimomura
Journal:

Canadian Mathematical Bulletin / Volume 65 / Issue 4 / December 2022

Published online by Cambridge University Press:

27 December 2021, pp. 924-935

Print publication:

December 2022
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Our aim in this paper is to establish Trudinger’s exponential integrability for Riesz potentials in weighted Morrey spaces on the half space. As an application, we obtain Trudinger’s inequality for Riesz potentials in the framework of double phase functionals.

SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES
Part of
- Linear function spaces and their duals
TAKAO OHNO, TETSU SHIMOMURA
Journal:

Journal of the Australian Mathematical Society / Volume 110 / Issue 3 / June 2021

Published online by Cambridge University Press:

02 October 2019, pp. 371-385

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June 2021
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Our aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials $J_{\unicode[STIX]{x1D6FC}(\cdot )}^{\unicode[STIX]{x1D70E}}f$ of functions $f$ in Musielak–Orlicz–Morrey spaces $L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705}}(X)$. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.

TIME AVERAGES FOR THE LAPLACE GROUP
Damian C. Jackson
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 1 / February 2005

Published online by Cambridge University Press:

15 February 2005, pp. 143-149
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The imaginary powers of the Laplace operator over the circle give a $C_0$ group of bounded linear operators on $\mathsf{L}_{\theta}^p(0,2\pi)$ ($1\ltp\lt\infty$). Whereas the group is unbounded on $\mathsf{L}^4$, this paper shows that the $\mathsf{L}^4$ long-time averages of each $f$ in $\mathsf{L}^2$ are bounded. This is a Fourier restriction phenomenon.
AMS 2000 Mathematics subject classification: Primary 42A15; 42B15

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3 results

Trudinger’s inequalities for Riesz potentials in Morrey spaces of double phase functionals on half spaces

SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES

TIME AVERAGES FOR THE LAPLACE GROUP