Analog of Hausdorff--Young theorem for quadratic--phase Fourier integral operators and boundedness of its convolution over weighted spaces
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Directly motivated by a recent result introduced by Castro et al. [\textit{Mediterr. J. Math.}, Vol. 15 (2018), article 13]. We establish the Hausdorff--Young type theorems for the quadratic--phase Fourier transform and its corresponding weighted convolution, which is the first aim of this paper. The second purpose of this work is to study the boundedness properties in a three-parameter family of positive measure-weighted Lebesgue spaces for this convolution via Young-type inequalities. The upper bounds of these inequalities are computed in detail via the Euler Gamma function.
Abstract
Directly motivated by a recent result introduced by Castro et al. [\textit{Mediterr. J. Math.}, Vol. 15 (2018), article 13]. We establish the Hausdorff--Young type theorems for the quadratic--phase Fourier transform and its corresponding weighted convolution, which is the first aim of this paper. The second purpose of this work is to study the boundedness properties in a three-parameter family of positive measure-weighted Lebesgue spaces for this convolution via Young-type inequalities. The upper bounds of these inequalities are computed in detail via the Euler Gamma function.