# $BL_{p,\nu}^{m}$ estimates for the Riesz transforms associated with Laplace-Bessel operator

Volume 11, Issue 6, pp 832--840
Publication Date: May 03, 2018 Submission Date: March 28, 2016 Revision Date: March 27, 2018 Accteptance Date: March 28, 2018
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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

•  47H10
•  45E10
•  47B37

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