scholarly journals Some sharp function estimates for vector-valued multilinear integral operator

2013 ◽  
Vol 14 (1) ◽  
pp. 373 ◽  
Author(s):  
Xiaosha Zhou
Keyword(s):  
Integral Operator ◽  
Sharp Function ◽  
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 Sharp function inequalities and boundness for Toeplitz type operator related to general fractional singular integral operator

2012 ◽  
Vol 92 (106) ◽  
pp. 165-176 ◽  
Author(s):  
Chuangxia Huang ◽  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Maximal Function ◽  
Type Operator ◽  
Sharp Maximal Function ◽  
Sharp Function ◽  
Toeplitz Type Operator

We establish some sharp maximal function inequalities for the Toeplitz type operator, which is related to certain fractional singular integral operator with general kernel. These results are helpful to investigate the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces respectively.

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

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.

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