\(L_{\alpha }^p\)-boundedness of the pseudo-differential operators associated with the Kontorovich-Lebedev transform

DOI10.1007/s13398-020-00812-8zbMath1441.47059OpenAlexW3001351976MaRDI QIDQ2293242

Santosh Kumar Upadhyay, M. S. Chauhan, Hari M. Srivastava

Publication date: 7 February 2020

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-020-00812-8

zbMATH Keywords

integral representationsKontorovich-Lebedev transformpseudo-differential operatorsMacdonald functionmodified Bessel function of the third kind\(L_{\alpha }^p\)-boundedness

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Pseudodifferential operators (47G30)

Related Items (9)

Abelian theorems for Laplace and Mehler-Fock transforms of generalized functions ⋮ Composition of wavelet transforms and wave packet transform involving Kontorovich-Lebedev transform ⋮ Product of pseudo-differential operators associated with zero order Mehler-Fock transform ⋮ The generalized Kontorovich-Lebedev transform and associated operators ⋮ Pseudo‐differential operator in quaternion space ⋮ A framework of linear canonical Hankel transform pairs in distribution spaces and their applications ⋮ Analytical investigation of nonlinear hybrid implicit functional differential inclusions of arbitrary fractional orders ⋮ An operational calculus for a Mehler-Fock type index transform on distributions of compact support ⋮ Boundedness of integral operators associated with the Kontorovich–Lebedev transform in the Lebesgue spaces type

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