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In this paper we establish decay estimates for Fourier transform onHardy-Morrey spaces and its localizable version. Our work include some aspectsto these spaces linked up with pointwise Fourier estimates, in particular anatural approach on cancellation moment conditions. As application, we discussthe optimality for continuity of Fourier multipliers and pseudodifferentialoperators in Hardy-Morrey spaces.

Fourier transform decay of distributions in Hardy-Morrey spaces