Boundedness of the Hausdorff operators in spaces, 0 < p < 1
Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces , 0 < p < 1, on the real line are proved. Two related negative results are also given.
Absolute convergence of multiple Fourier integrals
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.
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