Boundedness of vector-valuedB-singular integral operators in Lebesgue spaces

Seyda Keles, and Mehriban N. Omarova. "Boundedness of vector-valuedB-singular integral operators in Lebesgue spaces." Open Mathematics 15.1 (2017): 987-1002. <http://eudml.org/doc/288438>.

@article{SeydaKeles2017,
abstract = {We study the vector-valued B-singular integral operators associated with the Laplace-Bessel differential operator △B=∑k=1n−1∂ 2∂x k 2+(∂2∂x n 2+2vxn∂∂x n),v>0. \[\triangle \_\{B\}=\sum \limits \_\{k=1\}^\{n-1\}\frac\{\partial ^\{2\}\}\{\partial x\_\{k\}^\{2\}\}+(\frac\{\partial ^\{2\}\}\{\partial x\_\{n\}^\{2\}\}+\frac\{2v\}\{x\_\{n\}\}\frac\{\partial \}\{\partial x\_\{n\}\}) , v>0.\] We prove the boundedness of vector-valued B-singular integral operators A from [...] Lp,v(R+n,H1)toLp,v(R+n,H2), $L_\{p,v\}(\mathbb \{R\}_\{+\}^\{n\}, H_\{1\}) \,\{\rm to\}\, L_\{p,v\}(\mathbb \{R\}_\{+\}^\{n\}, H_\{2\}),$ 1 < p < ∞, where H1 and H2 are separable Hilbert spaces.},
author = {Seyda Keles, Mehriban N. Omarova},
journal = {Open Mathematics},
keywords = {Laplace-Bessel differential operator; Generalized shift operator; Vector-valued B-singular integral operators},
language = {eng},
number = {1},
pages = {987-1002},
title = {Boundedness of vector-valuedB-singular integral operators in Lebesgue spaces},
url = {http://eudml.org/doc/288438},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Seyda Keles
AU - Mehriban N. Omarova
TI - Boundedness of vector-valuedB-singular integral operators in Lebesgue spaces
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 987
EP - 1002
AB - We study the vector-valued B-singular integral operators associated with the Laplace-Bessel differential operator △B=∑k=1n−1∂ 2∂x k 2+(∂2∂x n 2+2vxn∂∂x n),v>0. \[\triangle _{B}=\sum \limits _{k=1}^{n-1}\frac{\partial ^{2}}{\partial x_{k}^{2}}+(\frac{\partial ^{2}}{\partial x_{n}^{2}}+\frac{2v}{x_{n}}\frac{\partial }{\partial x_{n}}) , v>0.\] We prove the boundedness of vector-valued B-singular integral operators A from [...] Lp,v(R+n,H1)toLp,v(R+n,H2), $L_{p,v}(\mathbb {R}_{+}^{n}, H_{1}) \,{\rm to}\, L_{p,v}(\mathbb {R}_{+}^{n}, H_{2}),$ 1 < p < ∞, where H1 and H2 are separable Hilbert spaces.
LA - eng
KW - Laplace-Bessel differential operator; Generalized shift operator; Vector-valued B-singular integral operators
UR - http://eudml.org/doc/288438
ER -