Sufficient conditions, of both smoothness and algebraic type, for the boundedness of multidimensional Hausdorff operators in Hardy spaces Hp(Rn), n ≥ 2, 0 < p < 1, are given. Positive and negative examples illustrate all aspects of the behavior of such operators and reveal the special nature of the case p < 1.
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© 2018 American Mathematical Society.
- Atomic decomposition
- Fourier transform
- Hardy space
- Hausdorff operator