Average sampling and reconstruction in a reproducing kernel subspace of homogeneous type space

2013 ◽  
Vol 287 (8-9) ◽  
pp. 1042-1056 ◽  
Author(s):  
Jun Xian
Keyword(s):  
Reproducing Kernel ◽  
Homogeneous Type ◽  
Type Space ◽  
Average Sampling ◽  
Sampling And Reconstruction ◽  
Homogeneous Type Space

scholarly journals ON LITTLEWOOD-PALEY FUNCTIONS ASSOCIATED WITH BESSEL OPERATORS

2009 ◽  
Vol 51 (1) ◽  
pp. 55-70 ◽  
Author(s):  
J. J. BETANCOR ◽  
J. C. FARIÑA ◽  
A. SANABRIA
Keyword(s):  
Higher Order ◽  
Doubling Measure ◽  
Homogeneous Type ◽  
Type Space ◽  
Bessel Operators ◽  
Homogeneous Type Space

AbstractIn this paper, we study Lp-boundedness properties for higher order Littlewood-Paley g-functions in the Bessel setting. We use the Calderón-Zygmund theory in a homogeneous-type space (in the sense of Coifman and Weiss) ((0, ∞), d, γα), where d represents the usual metric on (0, ∞) and γα denotes the doubling measure on (0, ∞) with respect to d defined by dγα(x) = x2α+1dx, with α > −1/2.

scholarly journals Calderón–Zygmund Operators Associated to Ultraspherical Expansions

2007 ◽  
Vol 59 (6) ◽  
pp. 1223-1244 ◽  
Author(s):  
Dariusz Buraczewski ◽  
Teresa Martinez ◽  
José L. Torrea
Keyword(s):  
Differential Operator ◽  
Higher Order ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Type Space ◽  
Ultraspherical Expansions ◽  
Homogeneous Type Space

AbstractWe define the higher order Riesz transforms and the Littlewood–Paley g-function associated to the differential operator Lλf(θ) = –f′′(θ)–2λ cot θ f′(θ) + λ2f(θ). We prove that these operators are Calderón–Zygmund operators in the homogeneous type space ((0, π), (sin t)2λdt). Consequently, Lp weighted, H1 – L1 and L∞ – BMO inequalities are obtained.

scholarly journals Average sampling in mixed shift-invariant subspaces with generators in hybrid-norm spaces

2021 ◽  
Author(s):  
Haizhen Li ◽  
Yan Tang
Keyword(s):  
Exponential Convergence ◽  
Invariant Subspaces ◽  
Time Varying ◽  
Projection Algorithms ◽  
Iterative Approximation ◽  
Wiener Amalgam Space ◽  
Average Sampling ◽  
Norm Space ◽  
Sampling And Reconstruction ◽  
Mixed Lebesgue Spaces

This paper mainly studies the average sampling and reconstruction in shift-invariant subspaces of mixed Lebesgue spaces $L^{p,q}(\mathbb{R}^{d+1})$, under the condition that the generator $\varphi$ of the shift-invariant subspace belongs to a hybrid-norm space of mixed form, which is weaker than the usual assumption of Wiener amalgam space and allows to control the orders $p,q$. First, the sampling stability for two kinds of average sampling functionals are established. Then, we give the corresponding iterative approximation projection algorithms with exponential convergence for recovering the time-varying shift-invariant signals from the average samples.

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