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

Seyda Keles; Mehriban N. Omarova

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 987-1002
- ISSN: 2391-5455

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topSeyda 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 -

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