TY - JOUR
T1 - Riesz transforms, Cauchy-Riemann systems and amalgam Hardy spaces
AU - Assaubay, Al Tarazi
AU - Betancor, Jorge J.
AU - Castro, Alejandro J.
AU - Fariña, Juan C.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this article 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 derivatives 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
AB - In this article 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 derivatives 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
KW - Amalgam spaces
KW - Cauchy-Riemann equations
KW - Hardy spaces
KW - Riesz transforms
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U2 - 10.1215/17358787-2018-0031
DO - 10.1215/17358787-2018-0031
M3 - Article
AN - SCOPUS:85073033350
VL - 13
SP - 697
EP - 725
JO - Banach Journal of Mathematical Analysis
JF - Banach Journal of Mathematical Analysis
SN - 1735-8787
IS - 3
ER -