\(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator
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Authors
Ismail Ekincioglu
- Department of Mathematics Kutahya, Dumlupnar University, Turkey.
Cansu Keskin
- Department of Mathematics Kutahya, Dumlupnar University, Turkey.
Serap Guner
- Department of Mathematics Kutahya, Dumlupnar University, Turkey.
Abstract
In this paper, we introduce higher order Riesz-Bessel transforms which
we can express partial derivatives of order \(\alpha\) of \(I_{m,\nu}f\) for \(f\in L_{p,\nu}\).
In addition, we establish relationship between Riesz potential
with higher order Riesz-Bessel transform related to generalized shift operator.
By using this relationship, we make some improvements of integral estimates
for \(I_{m,\nu}f\) and higher order Riesz-Bessel transform \(R_{\nu}^{m}\) in the
Beppo Levi space \(BL_{p,\nu}^{m}\). We prove an estimate for the singular integral operator with
convolution type generated by generalized shift operator in the Beppo Levi spaces.
Share and Cite
ISRP Style
Ismail Ekincioglu, Cansu Keskin, Serap Guner, \(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 6, 832--840
AMA Style
Ekincioglu Ismail, Keskin Cansu, Guner Serap, \(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator. J. Nonlinear Sci. Appl. (2018); 11(6):832--840
Chicago/Turabian Style
Ekincioglu, Ismail, Keskin, Cansu, Guner, Serap. "\(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator." Journal of Nonlinear Sciences and Applications, 11, no. 6 (2018): 832--840
Keywords
- Laplace-Bessel operator
- Bessel generalized shift operator
- Riesz-Bessel transform
- fractional integral operator
- Beppo Levi spaces
MSC
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