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151.
Multilinear singular integral operators with generalized kernels and their multilinear commutators 下载免费PDF全文
In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calderón–Zygmund operators and multilinear Calder′on–Zygmund operators with Dini type kernels. 相似文献
152.
153.
The paper proposes a unified approach to problems of stress concentration near notches with sharp and rounded tip based on
the method of singular integral equations. A solution for an elastic region having a V-shaped notch with rounded tip of large
curvature is first found. Then, the stress intensity factor at the tip of a sharp-tipped notch is calculated by passing to
the limit. Numerical results are obtained for a slit and a square hole in an elastic plane and an edge notch in a half-plane
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 70–87, February 2007.
For the centenary of the birth of G. N. Savin. 相似文献
154.
《Optimization》2012,61(9):1281-1288
In this article, we proved that the sequence generated by the proximal point method, associated to a unconstrained optimization problem in the Riemannian context, has finite termination when the objective function has a weak sharp minima on the solution set of the problem. 相似文献
155.
156.
Exact comparisons are made relating E|Y0|p, E|Yn−1|p, and E(maxj≤n−1 |Yj|p), valid for all martingales Y0,…,Yn−1, for each p ≥ 1. Specifically, for p > 1, the set of ordered triples {(x, y, z) : X = E|Y0|p, Y = E |Yn−1|p, and Z = E(maxj≤n−1 |Yj|p) for some martingale Y0,…,Yn−1} is precisely the set {(x, y, z) : 0≤x≤y≤z≤Ψn,p(x, y)}, where Ψn,p(x, y) = xψn,p(y/x) if x > 0, and = an−1,py if x = 0; here ψn,p is a specific recursively defined function. The result yields families of sharp inequalities, such as E(maxj≤n−1 |Yj|p) + ψn,p*(a) E |Y0|p ≤ aE |Yn−1|p, valid for all martingales Y0,…,Yn−1, where ψn,p* is the concave conjugate function of ψn,p. Both the finite sequence and infinite sequence cases are developed. Proofs utilize moment theory, induction, conjugate function theory, and functional equation analysis. 相似文献
157.
骆程 《浙江大学学报(理学版)》1996,23(3):226-229
当(u,ω)∈C时,我们证明了分布不等式ω(x∈R^n,Muf(x)〉Bf^#u(x)+λ)≤εω(x∈R^n,Muf(x)〉λ),(ε,λ〉0),其中B〉0与ε有关,f^#4,Muf分别是f关于测度udx的Sharp函和极大函数。 相似文献
158.
George A. Anastassiou Sorin G. Gal 《Journal of Computational Analysis and Applications》1999,1(1):3-23
In recent articles the first author and H. Gonska [e.g., see G. Anastassiou, C. Cottin, and H. Gonska, Global smoothness of approximating functions, Analysis, 11, 43–57 (1991); G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] studied global smoothness preservation by some univariate and multivariate linear operators over compact domains and
n
, n 1. In particular, they studied a very general positive linear integral type operator [e.g., see G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] over
n
that was introduced through a convolution-like integration of another general positive linear operator with a scaling-type function. In this article the authors, among others, extend and generalize [G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)]. Also certain new similar but more general integral operators are introduced and studied. These operators arise in a natural way, and for all these sufficient conditions are given for shift invariance, preservation of higher-order global smoothness and sharpness of the related inequalities, convergence to the unit using the first modulus of continuity, shape preservation, and preservation of continuous probabilistic distribution functions. Several examples of very general specialized operators, old and new, are given that satisfy all the above properties. 相似文献
159.
160.
An extension of the Gauss—Newton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization ofh F under two conditions, namelyh has a set of weak sharp minima,C, and there is a regular point of the inclusionF(x) C. This result extends a similar convergence result due to Womersley (this journal, 1985) which employs the assumption of a strongly unique solution of the composite functionh F. A backtracking line-search is proposed as a globalization strategy. For this algorithm, a global convergence result is established, with a quadratic rate under the regularity assumption.This material is based on research supported by National Science Foundation Grants CCR-9157632 and DMS-9102059, the Air Force Office of Scientific Research Grant F49620-94-1-0036, and the United States—Israel Binational Science Foundation Grant BSF-90-00455. 相似文献