Boundedness of generalized fractional integral operators on Orlicz spaces near L 1 over metric measure spaces

Daiki Hashimoto; Takao Ohno; Tetsu Shimomura

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 207-223
  • ISSN: 0011-4642

Abstract

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We are concerned with the boundedness of generalized fractional integral operators I ρ , τ from Orlicz spaces L Φ ( X ) near L 1 ( X ) to Orlicz spaces L Ψ ( X ) over metric measure spaces equipped with lower Ahlfors Q -regular measures, where Φ is a function of the form Φ ( r ) = r ℓ ( r ) and ℓ is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.

How to cite

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Hashimoto, Daiki, Ohno, Takao, and Shimomura, Tetsu. "Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces." Czechoslovak Mathematical Journal 69.1 (2019): 207-223. <http://eudml.org/doc/294775>.

@article{Hashimoto2019,
abstract = {We are concerned with the boundedness of generalized fractional integral operators $I_\{\rho ,\tau \}$ from Orlicz spaces $L^\{\Phi \}(X)$ near $L^1(X)$ to Orlicz spaces $L^\{\Psi \}(X)$ over metric measure spaces equipped with lower Ahlfors $Q$-regular measures, where $\Phi $ is a function of the form $\Phi (r)=r\ell (r)$ and $\ell $ is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.},
author = {Hashimoto, Daiki, Ohno, Takao, Shimomura, Tetsu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Orlicz space; Riesz potential; fractional integral; metric measure space; lower Ahlfors regular},
language = {eng},
number = {1},
pages = {207-223},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces},
url = {http://eudml.org/doc/294775},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Hashimoto, Daiki
AU - Ohno, Takao
AU - Shimomura, Tetsu
TI - Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 207
EP - 223
AB - We are concerned with the boundedness of generalized fractional integral operators $I_{\rho ,\tau }$ from Orlicz spaces $L^{\Phi }(X)$ near $L^1(X)$ to Orlicz spaces $L^{\Psi }(X)$ over metric measure spaces equipped with lower Ahlfors $Q$-regular measures, where $\Phi $ is a function of the form $\Phi (r)=r\ell (r)$ and $\ell $ is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.
LA - eng
KW - Orlicz space; Riesz potential; fractional integral; metric measure space; lower Ahlfors regular
UR - http://eudml.org/doc/294775
ER -

References

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