Some Inequalities for Singular Convolution Operators in L ^-spaces

  title={Some Inequalities for Singular Convolution Operators in L ^-spaces},
  author={Andreas Seeger},
Suppose that a bounded function m satisfies a localized multiplier condition sup(>0 ||^"n(tp-)llM„ < °°, f°r some bump function <p. We show that under mild smoothness assumptions m is a Fourier multiplier in Lp. The approach uses the sharp maximal operator and Littlewood-Paleytheory. The method gives new results for lacunary maximal functions and for multipliers in Triebel-Lizorkin-spaces. Introduction. Given a bounded function m the associated multiplier transformation Tm is defined by [Tm/]A… CONTINUE READING


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