The Journal of the Indian Mathematical Society

B. B. Waphare ¹

Affiliations
1 Maeer's Mit Arts, Commerce and Science College, Alandi (D), Talkhed, Pune 412 105, Maharashtra, IN

Abstract

In this paper we have defined Bessel-Hankel type spaces, Bochner-Riesz type means, the partial Hankel type integrals and these are used to obtain characterization of Besov-Hankel type spaces through the Bochner-Riesz type means and the partial Hankel type integrals.

Keywords

Hankel Type Transformation, Bochner-Riesz Type Means, Besov-Hankel Type Spaces, Partial Hankel Type Integrals.

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B. B. Waphare ¹

Affiliations
1 Maeer's Mit Art Commerce Science College, Alandi (D) TalKhed, Dist: Pune 412 105, Maharashtra, IN

Abstract

In this paper the generalized pseudo-differential type operator P(x,D), associated with the Bessel operator d²/dx² + (1-4α²-4β²+8αβ)/4x² is defined. The symbol class H^m_ρ,δ is introduced. It has been shown that the pseudo-differential type operator associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space H_α,β into itself. An integral representation of pseudo-differential type operator is obtained. Using Hankel type convolution,L^p_μ,a-norm continuity of the pseudo-differential type operator is proved.

Keywords

Pseudo-Differential Opearator, Bessel Type Operator, Integral Representation, Hankel Type Transformation, Generalized Pseudo-Differential Operators.

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