Boundedness in \(L_p\) spaces for the Hartley-Fourier convolutions operator and their applications

DOI10.1007/s10958-023-06422-0arXiv2306.12378OpenAlexW4383878165MaRDI QIDQ6147746

Trinh Tuan

Publication date: 1 February 2024

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.12378

zbMATH Keywords

convolutionsFredholm's integral equationsYoung's inequalities\(L_p\)-boundednessBarbashin's equationsHartley-Fourier transformsWiener-Tauberian's theorem

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Integro-ordinary differential equations (45J05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Convolution, factorization for one variable harmonic analysis (42A85) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Inequalities involving derivatives and differential and integral operators (26D10)

Cites Work

• Wave diffraction by a half-plane with an obstacle perpendicular to the boundary
• Operational properties of two integral transforms of Fourier type and their convolutions
• Operational properties of the Hartley convolution and its applications
• On the Fourier-sine and Kontorovich-Lebedev generalized convolution transforms and their applications
• On the Hartley - Fourier sine generalized convolution
• Evolutionary Integral Equations and Applications
• Boundedness in weighted L_p spaces for the Kontorovich–Lebedev–Fourier generalized convolutions and applications
• On Wiener’s Tauberian theorems and convolution for oscillatory integral operators
• Tauberian theorems
• Young inequalities for a Fourier cosine and sine polyconvolution and a generalized convolution
• Some results of Watson and Plancherel‐type integral transforms related to the Hartley, Fourier convolutions and applications
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