共查询到10条相似文献,搜索用时 15 毫秒
1.
In this paper, we study integral operators of the form Tαf(x)=∫Rn|x-A1y|-α1 ··· |x-Amy|-αmf(y)dy,where Ai are certain invertible matrices, αi 0, 1 ≤ i ≤ m, α1 + ··· + αm = n-α, 0 ≤α n. For 1/q = 1/p-α/n , we obtain the Lp (Rn, wp)-Lq(Rn, wq) boundedness for weights w in A(p, q) satisfying that there exists c 0 such that w(Aix) ≤ cw(x), a.e. x ∈ Rn , 1 ≤ i ≤ m.Moreover, we obtain theappropriate weighted BMO and weak type estimates for certain weights satisfying the above inequality. We also give a Coifman type estimate for these operators. 相似文献
2.
《数学物理学报(B辑英文版)》2020,(3)
In this article, we study the following critical problem involving the fractional Laplacian:■where ? ? R~N(N α) is a bounded smooth domain containing the origin, α∈(0, 2),0 ≤ s, t α, 1 ≤ q 2, λ 0, 2*_α(t) =2(N-t)/(N-α) is the fractional critical Sobolev-Hardy exponent, 0 ≤γ γH, and γH is the sharp constant of the Sobolev-Hardy inequality. We deal with the existence of multiple solutions for the above problem by means of variational methods and analytic techniques. 相似文献
3.
Long JIANG Department of Mathematics China University of Mining Technology Xuzhou Jiangsu China School of Mathematical Sciences Fudan University Shanghai China School of Mathematics System Sciences Shandong University Jinan China. 《数学年刊B辑(英文版)》2006,27(5)
Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen's inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) = 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen's inequality for g-expectation in [4, 7-9]. 相似文献
4.
ON UNIFORMLY VALID ESTIMATE OF SOLUTIONS TO SINGULAR PERTURBATION ROBIN BOUNDARY VALUE PROBLEM 总被引:1,自引:0,他引:1
In this paper we study the Robin boundary value problem with a small parameterεy″=f(t, y, ω(ε)y′, ε),a_0y(0) +b_0y′(0)=(ε), a_1y(1)+b_1y′(1)=η(ε),where the function ω(ε) is continuous on ε≥0 with ω(0)=0. Assuming all known functions are suitably smooth, f satisfies Nagumo's condition, f_y>0, a_t~2-b_t~2≠0, (-1)~ia_ib_i≤0 (i=0, 1) and the reduced equation 0=f(t, y, 0, 0) has a solution y(t) (0≤t≤1), we prove the existence and the uniqueness of the solution for the boundary value problem and givo an asymptotic expansion of the solution in the power ε~(1/2) which is uniformly valid on 0≤t≤1. 相似文献
5.
Sheng-jun Fan 《应用数学学报(英文版)》2009,25(1):11-20
Under the Lipschitz and square integrable assumptions on the generator g of BSDEs, this paper proves that if g is positively homogeneous in (y, z) and is decreasing in y, then the Moment inequality for BSDEs with generator g holds in general, and if g is positively homogeneous and sub-additive in (y, z), then the HSlder inequality and Minkowski inequality for BSDEs with generator g hold in general. 相似文献
6.
The well-known inequality of W.H.Young may be written as abintegral from 0 to a(Φ(x)dx)+integral from 0 to b(ψ(x)dx),where a>0,b>0,and Φ(x)∈C(0,∞) increases strictly with x and Φ(0)=0, andΨ(x) is the inverse function so that Ψ(Ф(x)=Ф(Ψ(x))=x.An investigation intothe graphs of the functions y=Φ(x) and x=Ψ(y) reveals that 相似文献
7.
Xie Chaodong 《Annals of Differential Equations》2006,22(1):69-74
In this paper, when μ< 1/4, and 2
0 and q=2(3-σ),the method is coming from the idea of Pohozaev. 相似文献
8.
Jian Wang 《数学学报(英文版)》2012,28(2):357-370
Criteria for the super-Poincaré inequality and the weak-Poincaré inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 (p. 15) of Prof. Mu-Fa Chen's book "Eigenvalues, Inequalities and Ergodic Theory" (Springer, London, 2005). As a byproduct, we conclude that only ergodic birth-death processes on finite state space satisfy the Nash inequality with index 0 ν≤ 2. 相似文献
9.
A sharp inequality for the tail probabilities of sums of i.i.d. r.v.’s with dominatedly varying tails 总被引:4,自引:0,他引:4
Let F be a distribution function supported on (-∞, ∞) with a finite mean μ. In this note weshow that if its tail F = 1 - F is dominatedly varying, then for any γ> max{μ, 0}, there exist C(γ) > 0 and D(γ) > 0 such thatC(γ)nF(x) ≤ Fn*(x) ≤ D(γ)nF(x),for all n ≥ 1 and all x ≥γn. This inequality sharpens a classical inequality for the subexponential distributioncase. 相似文献
10.
First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K,compute sequences xn, yxn, zxn such that { xn+1=(1-αn-rn)xn+αxPk[yn-ρTyn]+rnun,yn=(1-β-δn)xn+βnPk[zn-ηTxn]+δnun,zn=(1-an-λn)xn+akPk[xn-γTxn]+λnwn.For η, ρ,γ>0 are constants,{αn}, {βn}, {an}, {rn}, {δn}, {λn} C [0,1], {un}, {vn}, {wn} are sequences in K, and 0≤n + rn ≤ 1,0 ≤βn + δn ≤ 1,0 ≤ an + λn ≤ 1,(A)n ≥ 0, where T : K → H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems. 相似文献