| Title:
|
Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces (English) |
| Author:
|
Hashimoto, Daiki |
| Author:
|
Ohno, Takao |
| Author:
|
Shimomura, Tetsu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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69 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
207-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Orlicz space |
| Keyword:
|
Riesz potential |
| Keyword:
|
fractional integral |
| Keyword:
|
metric measure space |
| Keyword:
|
lower Ahlfors regular |
| MSC:
|
31B15 |
| MSC:
|
46E30 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 07088780 |
| idMR:
|
MR3923585 |
| DOI:
|
10.21136/CMJ.2018.0258-17 |
| . |
| Date available:
|
2019-03-08T15:00:28Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147628 |
| . |
| Reference:
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