A Note on Two Weight Inequalities for the Dyadic Paraproduct
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In this paper, we provide detailed proof of the Sawyer type characterization of the two weight estimate for the dyadic paraproduct. Although the dyadic paraproduct is known to be a well localized opera- tors and the testing conditions obtained from checking boundedness of the given localized operator on a collection of test functions are provided by many authors. The main purpose of this paper is to present the neces- sary and sufficient conditions on the weights to ensure boundedness of the dyadic paraproduct directly.
Abstract
In this paper, we provide detailed proof of the Sawyer type characterization of the two weight estimate for the dyadic paraproduct. Although the dyadic paraproduct is known to be a well localized opera- tors and the testing conditions obtained from checking boundedness of the given localized operator on a collection of test functions are provided by many authors. The main purpose of this paper is to present the neces- sary and sufficient conditions on the weights to ensure boundedness of the dyadic paraproduct directly.
참고문헌 (8)
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- E. T. Sawyer, "A characterization of a two weight norm inequality for maximal operators", Studia Math, 75, pp.1~11 (1982)
- S. Treil, "Operator-Related Function Theory and Time-Frequency Analysis", pp.185~195, Springer