Boundedness of the convolution operator in Lp(Zm) and smoothness of the symbol of the operator
Copyright policy )Boundedness of the convolution operator in Lp(Zm) and smoothness of the symbol of the operator
Sufficient conditions for the boundedness of the convolution operator in Lp(Zm) are found. These conditions are imposed on the symbol of the operator in terms of the spaces Hα and Hβ (functions of bounded variation of order β). The results obtained here generalize the results of S. B. Stechkin and I. I. Hirschman [Ref. Zh. Mat.7, No. 7821 (I960)] for the one-dimensional case.
- Southern Federal University Russian Federation
Integral, integro-differential, and pseudodifferential operators, smoothness of the symbol, Convolution, factorization for one variable harmonic analysis, convolution operator, boundedness
Integral, integro-differential, and pseudodifferential operators, smoothness of the symbol, Convolution, factorization for one variable harmonic analysis, convolution operator, boundedness
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