Sentence examples for variation operators for from inspiring English sources
We consider oscillation and variation operators for commutators of the Hilbert transform and Hermitian Riesz transform.
Recently, some authors [5 8] researched the weighted estimates of the oscillation and variation operators for the commutators of singular integrals.
The weighted ((L^{p}, L^{q}))-type estimates of the oscillation and variation operators for the iterated commutators will be given in Section 3.
As applications, the corresponding boundedness of the oscillation and variation operators for the commutators of Hilbert transform and the Hermitian Riesz transforms will be given.
In this paper, we will study the behaviors of oscillation and variation operators for the families of commutators defined by (1.7) and (1.8) in Lebesgue spaces.
The main purpose of this paper is to establish the weighted ((L^{p},L^{q})) inequalities of the oscillation and variation operators for the multilinear Calderón-Zygmund singular integral with a Lipschitz function.
The purpose of this paper is to establish some new results concerning the oscillation and ρ-variation operators for the families of commutators generated by Calderón-Zygmund singular integrals with Lipschitz functions.
Precisely, we will establish a criterion on the weighted ((L^{p}, L^{q}))-type estimates of the oscillation and ρ-variation operators for the iterated commutators of Calderón-Zygmund singular integrals with Lipschitz functions for (0<beta<1) and (1< p<1/beta) with (1/q=1/p-beta).
The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search.
We also remark that in our theorems, we deal only with (rho>2) for the variation operators, since in the case (rhole 2) the variation is often not bounded (see [1, 8]).
In all the experiments the variation operators are incorporated in a well-known algorithm usually considered as a reference for making the comparisons, the NSGA-II algorithm.
