Hypersingular Integrals and Their Applications

By S. Samko. 2001

305 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/bc1954571443082e5f1a09e67b057d8bca985eec

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Weyl and Marchaud Derivatives: A Forgotten History (2017, background): “General setting of Marchaud derivative and some further remarks The definition of Marchaud derivative, as it is known since [47], can be extended to all α > 0 in the following way, see [47] and [46].”
Sharp commutator estimates via harmonic extensions (2016, background): “[24, Corollary 1] who compute several explicit fractional Laplacians in terms of the Meijer G-function. As the authors informed us, special cases of (A.5) appear in the work of Samko, see for example [42]. It is also possible to obtain (A.5) from the Fourier representation (A.2). To obtain (A.4) fro”
Fractional integration and differentiation of variable order: an overview (2012, background): “lubny [37], Rubin [41], Samko [50], Samko, Kilbas”
Hardy inequality in the generalized Lebesgue spaces (2003, unknown): “where γn(α) = 2απ n 2 Γ(α2 ) Γ(n−α 2 ) (see for instance [20], p.”
Extension properties and boundary estimates for a fractional heat operator (2015, methodology): “in this note to characterize the nonlocal equation with a local degenerate parabolic equation. Using this in [ST] the authors prove a parabolic Harnack inequality and a version of the result of Salsa [Sa] referred to above. Subsequently, Ho¨lder and Schauder estimates for the space-time Poisson prob”
The Wiener algebra of absolutely convergent Fourier integrals: an overview (2012, background): “which is known to be expressed in terms of hyper-singular integrals, see [119] and [120].”
Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω (2004, background): “(the spherical Riesz potential operator, see [23], p.”
Fractional Laplace Operator and Meijer G-function (2015, background): “(34) This implies the following extension of expressions given in [24].”
Ten equivalent definitions of the fractional laplace operator (2015, background): “For the detailed analysis of Riesz potential operators Iα, we refer to [34, 38, 39, 42, 47].”