Some Inequalities for Integral Operators, Associated with the Bessel Differential Operator

Vagif S. Guliev ()
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Vagif S. Guliev: Institute of Mathematics and Mechanics Azerbaijan Academy of Sciences, Department of Mathematical Analysis

A chapter in Function Spaces, Differential Operators and Nonlinear Analysis, 2003, pp 317-328 from Springer

Abstract: Abstract In this paper we consider maximal functions, fractional maximal functions and fractional integrals which are generated by a generalized shift operator, associated with the Bessel differential operator $$B = (B_1 , \ldots ,B_n ),\;B_i = \frac{{\partial ^2 }} {{\partial x_i^2 }} + \frac{{\gamma _i }} {{x_i }}\frac{\partial } {{\partial x_i }},\;i = 1, \ldots ,n.$$ We present inequalities for these operators in corresponding weightedL p -spaces.In a special case we have found necessary and sufficient conditions for pairs of weights ensuring the validity of strong type inequalities for fractional integrals.

Keywords: Integral Operator; Maximal Function; Singular Integral; Fractional Integral; Homogeneous Type (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-8035-0_21

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DOI: 10.1007/978-3-0348-8035-0_21

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