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

Ekincioglu, Ismail ¹ ; Keskin, Cansu ¹ ; Guner, Serap ¹

¹ Department of Mathematics Kutahya, Dumlupnar University, Turkey

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 6, p. 832-840.

Résumé

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.

Détail

DOI : 10.22436/jnsa.011.06.09

Classification : 47H10, 45E10, 47B37
Keywords: Laplace-Bessel operator, Bessel generalized shift operator, Riesz-Bessel transform, fractional integral operator, Beppo Levi spaces

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