In this paper we study Hardy spaces Hp,q(Rd),
0<p,q<∞, modeled over amalgam spaces (Lp,ℓq)(Rd). We
characterize Hp,q(Rd) by using first order classical
Riesz transforms and compositions of first order Riesz transforms depending on
the values of the exponents p and q. Also, we describe the distributions in
Hp,q(Rd) as the boundary values of solutions of
harmonic and caloric Cauchy-Riemann systems. We remark that caloric
Cauchy-Riemann systems involve fractional derivative in the time variable.
Finally we characterize the functions in L2(Rd)∩Hp,q(Rd) by means of Fourier multipliers mθ
with symbol θ(⋅/∣⋅∣), where θ∈C∞(Sd−1) and Sd−1 denotes the unit sphere in
Rd.Comment: 24 page