The weighted Lp-boundedness of product-type pseudodifferential operators

Masao Yamazaki

doi:10.1016/0001-8708(89)90003-0

The weighted L^p-boundedness of product-type pseudodifferential operators

Masao Yamazaki^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper we consider non-regular simple symbols and double symbols satisfying estimates of product type, and give some sufficient conditions for the associated pseudodifferential operators to be bounded on weighted L^p-spaces, where the weights considered here are the A^q-weights of product type. In this paper we fill in the gap between the sufficient conditions for the unweighted L^p-boundedness and weighted L^p-boundedness. Some of the results are new even for the unweighted L^p-boundedness for symbols satisfying classical estimates.

Original language	English
Pages (from-to)	31-56
Number of pages	26
Journal	Advances in Mathematics
Volume	74
Issue number	1
DOIs	https://doi.org/10.1016/0001-8708(89)90003-0
Publication status	Published - 1989 Mar
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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title = "The weighted Lp-boundedness of product-type pseudodifferential operators",

abstract = "In this paper we consider non-regular simple symbols and double symbols satisfying estimates of product type, and give some sufficient conditions for the associated pseudodifferential operators to be bounded on weighted Lp-spaces, where the weights considered here are the Aq-weights of product type. In this paper we fill in the gap between the sufficient conditions for the unweighted Lp-boundedness and weighted Lp-boundedness. Some of the results are new even for the unweighted Lp-boundedness for symbols satisfying classical estimates.",

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AB - In this paper we consider non-regular simple symbols and double symbols satisfying estimates of product type, and give some sufficient conditions for the associated pseudodifferential operators to be bounded on weighted Lp-spaces, where the weights considered here are the Aq-weights of product type. In this paper we fill in the gap between the sufficient conditions for the unweighted Lp-boundedness and weighted Lp-boundedness. Some of the results are new even for the unweighted Lp-boundedness for symbols satisfying classical estimates.

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The weighted L^p-boundedness of product-type pseudodifferential operators

Abstract

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