scholarly journals The boundedness of variation associated with the commutators of approximate identities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yongming Wen ◽  
Xianming Hou
Keyword(s):  
Approximate Identities ◽  
Variation Operators ◽  
Heat Semigroups ◽  
Poisson Semigroups

AbstractIn this paper, we establish $L^{p}$ L p -boundedness and endpoint estimates for variation associated with the commutators of approximate identities, which are new for variation operators. As corollaries, we obtain the corresponding boundedness results for variation associated with the commutators of heat semigroups and Poisson semigroups.

Variational characterizations of weighted Hardy spaces and weighted spaces

2021 ◽  
pp. 1-20
Author(s):  
Weichao Guo ◽  
Yongming Wen ◽  
Huoxiong Wu ◽  
Dongyong Yang
Keyword(s):  
Hardy Spaces ◽  
Weighted Spaces ◽  
Weighted Hardy Spaces ◽  
Approximate Identities ◽  
Type Spaces ◽  
Variation Operators ◽  
Formula Type

This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.

scholarly journals On a family of weighted convolution algebras

1990 ◽  
Vol 13 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Hans G. Feichtinger ◽  
A. Turan Gürkanli
Keyword(s):  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Asymptotic Estimates ◽  
Locally Compact ◽  
Invariance Properties ◽  
Beurling Algebra ◽  
Convolution Algebras ◽  
Approximate Identities ◽  
Beurling Algebras ◽  
Banach Ideals

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebrasLw1(G),Ga locally compact Abelian group. These spaces are defined by weightedLp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

A criterion on oscillation and variation for the commutators of singular integral operators

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Weighted Norm ◽  
Norm Estimates ◽  
Variation Operators

AbstractThis paper gives a criterion on the weighted norm estimates of the oscillatory and variation operators for the commutators of Calderón–Zygmund singular integrals in dimension 1. As applications, the weighted

Emergent Tangled Program Graphs in Partially Observable Recursive Forecasting and ViZDoom Navigation Tasks

2021 ◽  
Vol 1 (3) ◽  
pp. 1-41
Author(s):  
Stephen Kelly ◽  
Robert J. Smith ◽  
Malcolm I. Heywood ◽  
Wolfgang Banzhaf
Keyword(s):  
Empirical Evaluation ◽  
Complete Information ◽  
Visual Navigation ◽  
Sources Of Information ◽  
Variation Operators ◽  
Incremental Construction ◽  
Partially Observable ◽  
First Person Shooter ◽  
With Memory ◽  
Program Graph

Modularity represents a recurring theme in the attempt to scale evolution to the design of complex systems. However, modularity rarely forms the central theme of an artificial approach to evolution. In this work, we report on progress with the recently proposed Tangled Program Graph (TPG) framework in which programs are modules. The combination of the TPG representation and its variation operators enable both teams of programs and graphs of teams of programs to appear in an emergent process. The original development of TPG was limited to tasks with, for the most part, complete information. This work details two recent approaches for scaling TPG to tasks that are dominated by partially observable sources of information using different formulations of indexed memory. One formulation emphasizes the incremental construction of memory, again as an emergent process, resulting in a distributed view of state. The second formulation assumes a single global instance of memory and develops it as a communication medium, thus a single global view of state. The resulting empirical evaluation demonstrates that TPG equipped with memory is able to solve multi-task recursive time-series forecasting problems and visual navigation tasks expressed in two levels of a commercial first-person shooter environment.

scholarly journals A class of factorable topological algebras

1990 ◽  
Vol 33 (1) ◽  
pp. 53-59 ◽  
Author(s):  
E. Ansari-Piri
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Approximate Identity ◽  
Necessary Condition ◽  
Topological Algebras ◽  
Approximate Identities ◽  
Cohen Factorization ◽  
Locally Convex ◽  
Space Property ◽  
Uniformly Bounded

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.

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