Linear and nonlinear Bessel potentials associated with the Poly-axially operator. Issue 4 (3rd April 2021)

• Record Type: Journal Article
• Authors: Selmi, Belgacem; Khelifi, Chahiba
• Is Part Of: Integral transforms and special functions. Volume 32:Issue 4(2021)
• Page Start: 316
• Page End: 331
• Publication Date: 2021-04-03
• Subjects: Fourier-Bessel transform -- Poly-axially operator -- Sobolev type spaces -- Bessel potential spaces -- nonlinear Bessel potential; 44A15 -- 46E35 -- 46F12; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2020.1825413
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: In this work, we will study a Bessel potential spaces W α s, p ( R + n ), ( s ∈ R, 1 ≤ p < + ∞, α = ( α 1, …, α n ) ∈ R n, α 1 > − 1 2, …, α n > − 1 2 ) associated with the Poly-axially operator Δ α and their properties. We define the Sobolev type spaces E α m, p ( R + n ) ( m ∈ N, 0 ∈ N, 1 ≤ p < + ∞ ) and we prove an analogue of Calderón's theorem for Fourier-Bessel transform. We define the nonlinear Bessel potentials associated with a measure ν and the L α p -capacity. Finally, we establish a classical problem of existence of an extremal function for the L α p -capacity.