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

In: Function Spaces, Differential Operators and Nonlinear Analysis

Author

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  • Vagif S. Guliev

    (Institute of Mathematics and Mechanics Azerbaijan Academy of Sciences, Department of Mathematical Analysis)

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.

Suggested Citation

  • Vagif S. Guliev, 2003. "Some Inequalities for Integral Operators, Associated with the Bessel Differential Operator," Springer Books, in: Dorothee Haroske & Thomas Runst & Hans-Jürgen Schmeisser (ed.), Function Spaces, Differential Operators and Nonlinear Analysis, pages 317-328, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-8035-0_21
    DOI: 10.1007/978-3-0348-8035-0_21
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