Lipschitz Estimate for Vector-valued Multilinear Commutator of Fractional Area Integral Operator

2014 ◽  
Vol 40 ◽  
pp. 305-314
Keyword(s):  
Integral Operator ◽  
Multilinear Commutator ◽  
Area Integral ◽  
Fractional Area ◽  
Lipschitz Estimate ◽  
Vector Valued

VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM

2006 ◽  
Vol 04 (04) ◽  
pp. 377-408 ◽  
Author(s):  
CLAUDIO CARMELI ◽  
ERNESTO DE VITO ◽  
ALESSANDRO TOIGO
Keyword(s):  
Integral Operator ◽  
Hilbert Spaces ◽  
Spectral Decomposition ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Integrable Functions ◽  
Kernel Hilbert Spaces ◽  
Vector Valued

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.

scholarly journals Area Integral Operator on the Real Unit Ball

2013 ◽  
Vol 03 (01) ◽  
pp. 56-67
Author(s):  
东方 王
Keyword(s):  
Integral Operator ◽  
Unit Ball ◽  
Area Integral ◽  
The Real

scholarly journals A substitution vector-valued integral operator

2015 ◽  
Vol 431 (2) ◽  
pp. 812-821 ◽  
Author(s):  
H. Emamalipour ◽  
M.R. Jabbarzadeh ◽  
Z. Moayyerizadeh
Keyword(s):  
Integral Operator ◽  
Vector Valued

scholarly journals Multiple Weighted Estimates for Vector-Valued Multilinear Singular Integrals with Non-Smooth Kernels and Its Commutators

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Dongxiang Chen ◽  
Dan Zou ◽  
Suzhen Mao
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Multilinear Commutator ◽  
Weighted Estimates ◽  
Bmo Functions ◽  
Multilinear Singular Integral Operator ◽  
Smooth Kernels ◽  
New Variant ◽  
Vector Valued ◽  
Multilinear Singular Integrals

This note concerns multiple weighted inequalities for vector-valued multilinear singular integral operator with nonsmooth kernel and its corresponding commutators containing multilinear commutator and iterated commutator generated by the vector-valued multilinear operator and BMO functions. By the weighted estimates for a class of new variant maximal and sharp maximal functions, the multiple weighted norm inequalities for such operators are obtained.

Application of integral operator for vector-valued regression learning

2015 ◽  
Vol 13 (06) ◽  
pp. 1550047 ◽  
Author(s):  
Yuanxin Ma ◽  
Hongwei Sun
Keyword(s):  
Hilbert Space ◽  
Integral Operator ◽  
Error Bounds ◽  
Learning Algorithm ◽  
Learning Performance ◽  
Operator Technique ◽  
Output Data ◽  
Learning Rates ◽  
Regression Learning ◽  
Vector Valued

In this paper, the regression learning algorithm with vector-valued RKHS is studied. We motivate the need for extending learning theory of scalar-valued functions and analze the learning performance. In this setting, the output data are from a Hilbert space [Formula: see text], the associated RKHS consists of functions with values lie in [Formula: see text]. By providing mathematical aspects of vector-valued integral operator [Formula: see text], the capacity independent error bounds and learning rates are derived by means of the integral operator technique.

scholarly journals Hyers-Ulam stability of substitution vector-valued integral operator

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6487-6492
Author(s):  
Zahra Moayyerizadeh
Keyword(s):  
Integral Operator ◽  
Conditional Expectation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ulam Stability ◽  
Necessary And Sufficient ◽  
Vector Valued

For a substitution vector-valued integral operator T?u, we determine necessary and sufficient conditions to have Hyers-Ulam stability using conditional expectation operators. Then, we present an example to illustrate our result.

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