Alberto Debernardi Pinos

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math.CA2023

Weighted norm inequalities for integral transforms with splitting kernels

Alberto Debernardi Pinos

We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^{p} - L^{q}$ spaces, with $1 \leq p \leq q \leq \infty$ . T…

math.CA2023

Fourier inequalities in Morrey and Campanato spaces

Alberto Debernardi Pinos, Erlan Nursultanov, Sergey Tikhonov

We study norm inequalities for the Fourier transform, namely, \begin{equation}\label{introduction} \|\widehat f\|_{X_{p,q}^λ} \lesssim \|f\|_{Y}, \end{equation} where $X$ is either…

math.CA2023

Nuclearity and Grothendieck-Lidskii formula for quaternionic operators

Paula Cerejeiras, Fabrizio Colombo, Alberto Debernardi Pinos +2

We introduce an appropriate notion of trace in the setting of quaternionic linear operators, arising from the well-known companion matrices. We then use this notion to define the q…