Banach Journal of Mathematical Analysis

Riesz transforms, Cauchy–Riemann systems, and Hardy-amalgam spaces

Al-Tarazi Assaubay, Jorge J. Betancor, Alejandro J. Castro, and Juan C. Fariña

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In this article we study Hardy spaces Hp,q(Rd), 0<p,q<, modeled over amalgam spaces (Lp,q)(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 θC(Sd1) and Sd1 denotes the unit sphere in Rd.

Article information

Banach J. Math. Anal., Volume 13, Number 3 (2019), 697-725.

Received: 5 June 2018
Accepted: 2 October 2018
First available in Project Euclid: 25 May 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B30: $H^p$-spaces
Secondary: 42B35: Function spaces arising in harmonic analysis

Hardy spaces amalgam spaces Cauchy–Riemann equations Riesz transforms


Assaubay, Al-Tarazi; Betancor, Jorge J.; Castro, Alejandro J.; Fariña, Juan C. Riesz transforms, Cauchy–Riemann systems, and Hardy-amalgam spaces. Banach J. Math. Anal. 13 (2019), no. 3, 697--725. doi:10.1215/17358787-2018-0031.

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