%0 Journal Article
%T \(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator
%A Ekincioglu, Ismail
%A Keskin, Cansu
%A Guner, Serap
%J Journal of Nonlinear Sciences and Applications
%D 2018
%V 11
%N 6
%@ ISSN 2008-1901
%F Ekincioglu2018
%X 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.
%9 journal article
%R 10.22436/jnsa.011.06.09
%U http://dx.doi.org/10.22436/jnsa.011.06.09
%P 832--840