NewLp-boundedness properties for the Kontorovich–Lebedev and Mehler–Fock transforms

DOI10.1080/10652469.2016.1221952zbMath1360.44005OpenAlexW2530947135MaRDI QIDQ5506802

Emilio R. Negrin, Benito J. González, Hari M. Srivastava

Publication date: 16 December 2016

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2016.1221952

zbMATH Keywords

Hölder's inequalityKontorovich-Lebedev transformMehler-Fock transformassociated Legendre function\(L^p\)-boundedness propertiesmodified Bessel (or the Macdonald) function

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Related Items (21)

Lebedev–Skalskaya transforms and allied operators on certain function spaces ⋮ Continuous wavelet transform associated with zero-order Mehler–Fock transform and its composition ⋮ The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces ⋮ Abelian theorems for Laplace and Mehler-Fock transforms of generalized functions ⋮ Composition of wavelet transforms and wave packet transform involving Kontorovich-Lebedev transform ⋮ The localization operator and wavelet multipliers involving the Watson transform ⋮ Product of pseudo-differential operators associated with zero order Mehler-Fock transform ⋮ The generalized Kontorovich-Lebedev transform and associated operators ⋮ The convolution for zero-order Mehler–Fock transform and pseudo-differential operator ⋮ Abelian theorems for fractional wavelet transform ⋮ The Lambert transform over distributions of compact support, \(L^1\)-functions and Boehmian spaces ⋮ The Kontorovich-Lebedev transform and Sobolev type space ⋮ \(L_{\alpha }^p\)-boundedness of the pseudo-differential operators associated with the Kontorovich-Lebedev transform ⋮ Zero-order Mehler-Fock transform and Sobolev-type space ⋮ Abelian theorems for distributional Kontorovich-Lebedev and Mehler-Fock transforms of general order ⋮ L2-boundedness and L2-compactness of a class of semiclassical Fourier integral operators with operator symbol ⋮ Lebedev–Skalskaya transforms on certain function spaces and associated pseudo-differential operators ⋮ 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 ⋮ On operators with complex Gaussian kernels over Lp spaces ⋮ On an inversion formula for the fourier transform on distributions by means of Gaussian functions

Cites Work

• Unnamed Item
• On the least values of \(L_{p}\)-norms for the Kontorovich--Lebedev transform and its convolution
• On the Kontorovich-Lebedev transformation
• Boundedness properties for a class of integral operators including the index transforms and the operators with complex Gaussian kernels
• On the Mehler‐Fock Transform in L_p‐Space
• A family of Wiener transforms associated with a pair of operators on Hilbert space
• Analog of the Hausdorff–Young theorem for the Lebedev integral

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