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.
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Guliev, V.S. (2003). Some Inequalities for Integral Operators, Associated with the Bessel Differential Operator. In: Haroske, D., Runst, T., Schmeisser, HJ. (eds) Function Spaces, Differential Operators and Nonlinear Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8035-0_21
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DOI: https://doi.org/10.1007/978-3-0348-8035-0_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9414-2
Online ISBN: 978-3-0348-8035-0
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