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July 2019 Riesz transforms, Cauchy–Riemann systems, and Hardy-amalgam spaces
Al-Tarazi Assaubay, Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña
Banach J. Math. Anal. 13(3): 697-725 (July 2019). DOI: 10.1215/17358787-2018-0031

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.

Citation

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

Information

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

zbMATH: 07083768
MathSciNet: MR3978944
Digital Object Identifier: 10.1215/17358787-2018-0031

Subjects:
Primary: 42B30
Secondary: 42B35

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 3 • July 2019
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