Decomposition of Besov Spaces

Frazier, Michael; Werth, Björn Ja

doi:10.1515/9781400827268.385

Cited by 164 publications

(315 citation statements)

References 12 publications

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“…That is, the "function space" component and the "sequence space" component of F We use the ϕ-ψ transform introduced by Frazier and Jawerth in [22,23,24,25].…”

Section: Y)mentioning

confidence: 99%

Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces

2012

Ann. Acad. Sci. Fenn. Math.

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Abstract. A criteria on the vector-valued Banach function spaces X (B) is obtained so that whenever a vector-valued singular integral operator is bounded on X (B), it can be extended to be a bounded linear operator on the corresponding Morrey type spaces. Using this result, we define the generalized Triebel-Lizorkin-Morrey spaces and obtain the atomic and molecular decompositions. As a particular example of the generalized Triebel-Lizorkin-Morrey spaces, we introduce and study the variable Triebel-Lizorkin-Morrey spaces.

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“…That is, the "function space" component and the "sequence space" component of F We use the ϕ-ψ transform introduced by Frazier and Jawerth in [22,23,24,25].…”

Section: Y)mentioning

confidence: 99%

Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces

2012

Ann. Acad. Sci. Fenn. Math.

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“…In the context of Sobolev and Besov spaces the method goes back to the seminal papers by M. Frazier and B. Jawerth, cf. [6,7]. The atomic decomposition adapted to the radial case was constructed by J. Epperson and M. Frazier in [5].…”

Section: Preparations: Atomic Decompositionmentioning

confidence: 99%

Pointwise Estimates for Block-Radial Functions of Sobolev Classes

Skrzypczak

Tintarev

2018

J Fourier Anal Appl

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The paper gives sharp pointwise estimates for functions belonging tȯ H s, p (R N ) with radial symmetry in m blocks of variables, for m < sp < N . The estimates are formulated in terms of multiradial monomials. The form of the monomials depends on the structure of the group of block-radial symmetries and the distances of the given point to the hyperplanes in R N that contain the singular orbits of the group. For some exceptional set of parameters the logarithmic factor is needed. Weak continuity related to the estimates is also considered.

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“…Hence yk= a*y0+b*y1+… (15) In terms of the differentials of the previous output, it becomes yk =b1*yk-1+c1d(yk-1)/dt (16) c1 being a constant Here the incremental portion will be approximated as the convolution of some function with y0. (18) Since the response is delayed by N/2.N being the no. of points in Fourier transform.…”

Section: Convolution Of Hyperplanesmentioning

confidence: 99%

Differential Learning Algorithm for Artificial Neural Networks

Manjunath¹,

Vasudev²,

Udupa³

2010

IJCA

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Artificial Neural Networks (ANN) are extremely useful to relate the nonlinearly depending outputs with the inputs. Various architectures are available for the ANNs to speedup the training period and reduce the square error. In this paper, new classes of neural networks with differential feedback are presented. The different orders of differential feed back form a manifold of hyperplanes. Interesting properties of this differentially fed ANN (DANN) are derived through these hyperplanes.

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Decomposition of Besov Spaces

Cited by 164 publications

References 12 publications

Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces

Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces

Pointwise Estimates for Block-Radial Functions of Sobolev Classes

Differential Learning Algorithm for Artificial Neural Networks

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