Fourier Spectrum Characterizations of Hardy Spaces $$H^p$$ on Tubes for $$0<p<1$$

Abstract

As continuation of the study of Fourier spectrum characterization of higher-dimensional Hardy spaces $$H^p(T_{\Gamma })$$ on tubes for $$1\le p\le \infty $$ , this paper aims to obtain analogous Fourier spectrum characterizations and integral representation formulas of higher-dimensional Hardy spaces $$H^p(T_{\Gamma })$$ on tubes for the index range $$0< p < 1$$ . For $$1\le p\le \infty $$ , the $$H^p(T_{\Gamma })$$ are well understood via the Poisson and conjugate Poisson integrals. However, for $$0< p < 1$$ , those integrals are no longer defined that requires more delicate analysis.