The Hadamard–Bergman Convolution on the Half-Plane

We introduce the Hadamard–Bergman convolution on the half-plane. We show that it exists in terms of the Hadamard product and it is commutative on the Bergman space (more appropriately called the Bergman–Jerbashian space) in the half-plane. Further, we explore mapping properties of the generalized Be...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2024-08, Vol.30 (4), Article 38
Main Authors: Karapetyants, Alexey, Vagharshakyan, Armen
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Convolution
Fourier Analysis
Half planes
Inclusions
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial Differential Equations
Signal,Image and Speech Processing
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Summary:We introduce the Hadamard–Bergman convolution on the half-plane. We show that it exists in terms of the Hadamard product and it is commutative on the Bergman space (more appropriately called the Bergman–Jerbashian space) in the half-plane. Further, we explore mapping properties of the generalized Bergman-type operators with exponential weights in weighted Bergman spaces in the half-plane. Finally, we deduce sharp inclusions for weighted Bergman spaces, from corresponding Sobolev-type inequalities.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-024-10097-9