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FRACTIONAL INTEGRAL OPERATORS ON $\unicode[STIX]{x1D6FC}$-MODULATION SPACES IN THE FULL RANGE

Part of: Harmonic analysis in several variables Integral, integro-differential, and pseudodifferential operators

Published online by Cambridge University Press:  28 March 2018

GUOPING ZHAO ,
WEICHAO GUO Open the ORCID record for WEICHAO GUO [Opens in a new window]  and
XIAO YU
GUOPING ZHAO
Affiliation:
School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, PR China email guopingzhaomath@gmail.com
WEICHAO GUO*
Affiliation:
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, PR China email weichaoguomath@gmail.com
XIAO YU
Affiliation:
Department of Mathematics, Shangrao Normal University, Shangrao, 334001, PR China email yx2000s@163.com
*
✉weichaoguomath@gmail.com
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Abstract

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We use a unified approach to study the boundedness of fractional integral operators on $\unicode[STIX]{x1D6FC}$-modulation spaces and find sharp conditions for boundedness in the full range.

Keywords

fractional integral operatorsmodulation space𝛼-modulation spaceBesov spacesharp conditions

MSC classification

Primary: 47G40: Potential operators
Secondary: 42B15: Multipliers 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 3 , June 2018 , pp. 499 - 512
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work is partially supported by the National Natural Science Foundation of China (nos. 11601456, 11701112, 11671414, 11771388, 11371316), China Postdoctoral Science Foundation (no. 2017M612628) and the Natural Science Foundation of Jiangxi Province (no. 20151BAB211002).

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