In this article we study Hardy spaces , , modeled over amalgam spaces . We characterize by using first-order classical Riesz transforms and compositions of first-order Riesz transforms, depending on the values of the exponents and . Also, we describe the distributions in as the boundary values of solutions of harmonic and caloric Cauchy–Riemann systems. We remark that caloric Cauchy–Riemann systems involve fractional derivatives in the time variable. Finally, we characterize the functions in by means of Fourier multipliers with symbol , where and denotes the unit sphere in .
"Riesz transforms, Cauchy–Riemann systems, and Hardy-amalgam spaces." Banach J. Math. Anal. 13 (3) 697 - 725, July 2019. https://doi.org/10.1215/17358787-2018-0031