Sobolev-type spaces E^{s,p}_α are introduced for the poly-axially operator using the Fourier-Bessel transform, with completeness, embeddings, Reillich compactness, and Poincaré inequality, all as adaptations of known univariate theories.
and El Garna A.: Properties of the linear multiplier operat or for the Weinstein transform and applications, Electronic Journal of Differential Equations, 124, 1-18 (2017)
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Sobolev type spaces associated with the Poly-axially operator
Sobolev-type spaces E^{s,p}_α are introduced for the poly-axially operator using the Fourier-Bessel transform, with completeness, embeddings, Reillich compactness, and Poincaré inequality, all as adaptations of known univariate theories.