TY - JOUR AU - Ekincioglu, Ismail AU - Keskin, Cansu AU - Guner, Serap PY - 2018 TI - \(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator JO - Journal of Nonlinear Sciences and Applications SP - 832--840 VL - 11 IS - 6 AB - 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. 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