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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1558749976

Digital Object Identifier
doi:10.1215/17358787-2018-0031

Mathematical Reviews number (MathSciNet)
MR3978944

Zentralblatt MATH identifier
07083768

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

Keywords
Hardy spaces amalgam spaces Cauchy–Riemann equations Riesz transforms

Citation

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. https://projecteuclid.org/euclid.bjma/1558749976


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