Weighted inequalities for rough square functions through extrapolation

Abstract

Abstract. Weighted inequalities for some square functions are studied. L 2 results are proved first using the particular structure of the operator and then extrapolation of weights is applied to extend the results to other L p spaces. In particular, previous results for square functions with rough kernel are obtained in a simpler way and extended to a larger class of weights. Introduction. Littlewood-Paley and Marcinkiewicz type operatorsare given by square functions. For a historical overview of this topic and its several aspects the reader can consult the paper by E. Stein [15]. A typical case is the following: given a function N in R n satisfying appropriate conditions, define N t (x) = t −n N (t −1 x) for t > 0 and construct the square function

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