共查询到20条相似文献,搜索用时 0 毫秒
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Vittorino Pata 《Journal of Mathematical Analysis and Applications》2011,373(1):264-270
We discuss a Gronwall-type lemma depending on a small parameter ε>0, based on an integral inequality that predicts blow-up in finite time of the involved unknown function for any fixed ε. The result permits to establish uniform estimates even if the function itself depends on ε. 相似文献
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V. V. Listopad 《Ukrainian Mathematical Journal》1993,45(6):863-870
Uniform estimates are obtained for the monotone approximation of the functions from the generalized Babenko classes.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 785–790, June, 1993. 相似文献
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Árpad Bényi Diego Maldonado Andrea R. Nahmod Rodolfo H. Torres 《Mathematische Nachrichten》2010,283(9):1257-1276
Boundedness properties for bilinear paraproducts on several function spaces are presented. The methods are based on the realization of paraproducts as bilinear Calderón‐Zygmund operators and the molecular character‐ization of function spaces. This provides a unified approach for the study of paraproducts, recovering some know results and establishing several new (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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In a previous paper [20] in this series, we gaveL
p estimates for multi-linear operators given by multipliers which are singular on a non-degenerate subspace of some dimensionk. In this paper, we give uniform estimates when the subspace approaches a degenerate region in the casek = 1, and when all the exponentsp are between 2 and ∞. In particular, we recover the non-endpoint uniform estimates for the bilinear Hubert transform in [12].
Dedicated to Tom Wolff 相似文献
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Journal of Fourier Analysis and Applications - 相似文献
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The uniform estimate is established for a monotone polynomial approximation of functions whose smoothness decreases at the ends of a segment.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 38–43, January, 1993. 相似文献
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Philip T. Gressman 《Journal d'Analyse Mathématique》2011,115(1):251-272
This paper reconsiders the uniform sublevel set estimates of Carbery, Christ, and Wright [7], Phong, Stein, and Sturm [23], and Carbery and Wright [8] from a geometric perspective. This perspective leads one to consider a natural collection of homogeneous, nonlinear differential
operators, which generalize mixed derivatives in ℝ
d
. As a consequence, it is shown that, in comparison to these previous works, improved uniform estimates are possible in all
but certain explicitly “flat” situations. 相似文献
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V. N. Karpushkin 《Siberian Mathematical Journal》1989,30(2):240-249
Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 2, pp. 90–101, March–April, 1989. 相似文献
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E. J. Scourfield 《Monatshefte für Mathematik》1984,97(3):233-247
Leta (n) denote a multiplicative function taking the values 0, 1 only, and suppose that the setP of primesp witha (p)=1 has density (P)(0<(P)<1). Using sieve results, upper and lower bounds of essentially the same order of magnitude are obtained for #{nxa(n)=1}, their dependence onP being made explicit. Bounds, uniform for squarefreed in an extensive range, for #{nx(d,f(n))=1} withf a multiplicative function in a class containing Euler's function are then deduced. 相似文献
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Maria Manfredini 《Annali di Matematica Pura ed Applicata》2009,188(3):417-428
In this paper we are concerned with a family of elliptic operators represented as sum of square vector fields: in , where Δ is the Laplace operator, m < n, and the limit operator is hypoelliptic. Here we establish Schauder’s estimates, uniform with respect to the parameter ϵ, of solution of the approximated
equation L
ϵ
u = f, using a modification of the lifting technique of Rothschild and Stein. These estimates can be used in particular while studying
regularity of viscosity solutions of nonlinear equations represented in terms of vector fields.
相似文献
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We prove new estimates for spherical functions and their derivatives on complex semisimple Lie groups, establishing uniform
polynomial decay in the spectral parameter. This improves the customary estimate arising from Harish-Chandra's series expansion,
which gives only a polynomial growth estimate in the spectral parameter. In particular, for arbitrary positive-definite spherical
functions on higher rank complex simple groups, we establish estimates for which are of the form in the spectral parameter and have uniform exponential decay in regular directions in the group variable a
t
. Here is an explicit constant depending on G, and may be singular, for instance.?The uniformity of the estimates is the crucial ingredient needed in order to apply classical
spectral methods and Littlewood—Paley—Stein square functions to the analysis of singular integrals in this context. To illustrate
their utility, we prove maximal inequalities in L
p
for singular sphere averages on complex semisimple Lie groups for all p in . We use these to establish singular differentiation theorems and pointwise ergodic theorems in L
p
for the corresponding singular spherical averages on locally symmetric spaces, as well as for more general measure preserving
actions.
Submitted: May 2000, Revised version: October 2000. 相似文献
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Jeffery D. McNeal 《Proceedings of the American Mathematical Society》2002,130(1):39-47
We show that a uniform subelliptic estimate for the -Neumann problem holds on a certain family of convex domains of finite type.
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Thierry Cazenave 《Journal of Functional Analysis》1985,60(1):36-55
Uniform estimates in of global solutions to nonlinear Klein-Gordon equations of the form , where Ω is an open subset of N, m > 0, and g satisfies some growth conditions are established. 相似文献
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We establish uniform estimates for order statistics: Given a sequence of independent identically distributed random variables
ξ
1, … , ξ
n
and a vector of scalars x = (x
1, … , x
n
), and 1 ≤ k ≤ n, we provide estimates for
\mathbb E k-min1 £ i £ n |xixi|{\mathbb E \, \, k-{\rm min}_{1\leq i\leq n} |x_{i}\xi _{i}|} and
\mathbb E k-max1 £ i £ n|xixi|{\mathbb E\,k-{\rm max}_{1\leq i\leq n}|x_{i}\xi_{i}|} in terms of the values k and the Orlicz norm ||yx||M{\|y_x\|_M} of the vector y
x
= (1/x
1, … , 1/x
n
). Here M(t) is the appropriate Orlicz function associated with the distribution function of the random variable |ξ
1|,
G(t) = \mathbb P ({ |x1| £ t}){G(t) =\mathbb P \left(\left\{ |\xi_1| \leq t\right\}\right)}. For example, if ξ
1 is the standard N(0, 1) Gaussian random variable, then
G(t) = ?{\tfrac2p}ò0t e-\fracs22ds {G(t)= \sqrt{\tfrac{2}{\pi}}\int_{0}^t e^{-\frac{s^{2}}{2}}ds } and
M(s)=?{\tfrac2p}ò0se-\frac12t2dt{M(s)=\sqrt{\tfrac{2}{\pi}}\int_{0}^{s}e^{-\frac{1}{2t^{2}}}dt}. We would like to emphasize that our estimates do not depend on the length n of the sequence. 相似文献
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Luis Caffarelli Enrico Valdinoci 《Calculus of Variations and Partial Differential Equations》2011,41(1-2):203-240
We consider nonlocal minimal surfaces obtained by a fractional type energy functional, parameterized by ${s\in(0,1)}$ . We show that the s-energy approaches the perimeter as s ?? 1?. We also provide density properties and clean ball conditions, which are uniform as s ?? 1?, and optimal lower bounds obtained by a rearrangement result. Then, we show that s-minimal sets approach sets of minimal perimeter as s ?? 1?. 相似文献
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Giona Veronelli 《Geometriae Dedicata》2011,155(1):1-20
We study positive solutions u of the Yamabe equation
cm Du-s( x) u+k( x) u\fracm+2m-2=0{c_{m} \Delta u-s\left( x\right) u+k\left( x\right) u^{\frac{m+2}{m-2}}=0}, when k(x) > 0, on manifolds supporting a Sobolev inequality. In particular we get uniform decay estimates at infinity for u which depend on the behaviour at infinity of k, s and the L
Γ-norm of u, for some
G 3 \tfrac2mm-2{\Gamma\geq\tfrac{2m}{m-2}}. The required integral control, in turn, is implied by further geometric conditions. Finally we give an application to conformal
immersions into the sphere. 相似文献
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Let be a domain with a Jordan boundary ∂G, consisting of l smooth curves Γj, such that {zj}Γj-1∩Γj≠, j=1,…,l, where Γ0Γl. Denote by αjπ, 0<αj2, the angles at zj's between the curves Γj-1 and Γj, exterior with respect to G. Let Φ be a conformal mapping of the exterior of onto the exterior of the unit disk, normed by Φ′(∞)>0. We assume that there is a neighborhood U of , such that , wherez≠zj if αj1. Set gGsup{|g(z)|:zG}. Then we prove Theorem. Let and 0βr. If a function f is analytic in G and f(r)βG<+∞, then for each nlr there is an algebraic polynomial Pn of degree <n, such that 相似文献