共查询到20条相似文献,搜索用时 15 毫秒
1.
Christopher D. Sinclair 《Monatshefte für Mathematik》2012,166(1):121-144
We give a hyperpfaffian formulation of partition functions and ensemble averages for Hermitian and circular ensembles when L is an arbitrary integer and ???=?L 2 and when L is an odd integer and ???=?L 2?+?1. 相似文献
2.
We study hereL 1-convergence of a complex trigonometric sum and obtain a new necessary and sufficient condition for theL 1-convergence of Fourier series. 相似文献
3.
We consider singular integral operators of the form (a)Z 1L?1Z2, (b)Z 1Z2L?1, and (c)L ?1Z1Z2, whereZ 1 andZ 2 are nonzero right-invariant vector fields, andL is theL 2-closure of a canonical Laplacian. The operators (a) are shown to be bounded onL p for allp∈(1, ∞) and of weak type (1, 1), whereas all of the operators in (b) and (c) are not of weak type (p, p) for anyp∈[1, ∞). 相似文献
4.
We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for L 1[0,1] d (d≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all f∈L 1[0,1] d . 相似文献
5.
Daniel E Wulbert 《Journal of Functional Analysis》1975,19(3):205-215
Our results are related to 1-shadows in Lp-spaces. For p = 1 we will complete the characterization of 1-shadows and 1,1-shadows. For 1 < p < ∞ S. J. Bernau has shown that the 1-shadow of a set in Lp is the range of a contractive projection. We will show that the corresponding theorem is not true for all reflexive spaces, but is true for locally uniformly convex reflexive spaces. 相似文献
6.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(10):939-943
We present a non-diffusive scheme using a flux-limiter approach. This limiter verifies L∞-stability and TVD conditions. The convergence is established. We identify a class of functions (dense in L1) that are advected exactly. 相似文献
7.
Michael Ruzhansky 《Results in Mathematics》2002,41(3-4):361-368
In this paper we consider the Cauchy problem for a class of hyperbolic pseudodifferential operators. The considered class contains constant coefficient differential equations, also allowing the coefficients to depend on time. We establish sharp L p ? Lp, Lipschitz, and other estimates for their solutions. In particular, the ellipticity condition for the roots of the principal symbol is eliminated for certain dimensions. We discuss the situation with no loss of smoothness for solutions. In the space R1+n with n ≤ 4 (total dimension ≤ 5), we give a complete list of L p ? Lp properties. In particular, this contains the very important case R1+3. 相似文献
8.
Here we introduce a subclass of the class of Ockham algebras ( L ; f ) for which L satisfies the property that for every x ∈ L , there exists n ≥ 0 such that fn ( x ) and fn+1 ( x ) are complementary. We characterize the structure of the lattice of congruences on such an algebra ( L ; f ). We show that the lattice of compact congruences on L is a dual Stone lattice, and in particular, that the lattice Con L of congruences on L is boolean if and only if L is finite boolean. We also show that L is congruence coherent if and only if it is boolean. Finally, we give a sufficient and necessary condition to have the subdirectly irreducible chains. 相似文献
9.
Eleftherios N. Nikolidakis 《Journal of Fourier Analysis and Applications》2013,19(1):115-139
We obtain sharp estimates for the localized distribution function of $\mathcal{M}\phi $ , when ? belongs to L p,∞ where $\mathcal{M}$ is the dyadic maximal operator. We obtain these estimates given the L 1 and L q norm, q<p and certain weak-L p conditions.In this way we refine the known weak (1,1) type inequality for the dyadic maximal operator. As a consequence we prove that the inequality 0.1 is sharp allowing every possible value for the L 1 and the L q norm for a fixed q such that 1<q<p, where ∥?∥ p,∞ is the usual quasi norm on L p,∞. 相似文献
10.
Let(X,d,μ)be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of Hyto¨nen.We prove that the L p(μ)-boundedness with p∈(1,∞)of the Marcinkiewicz integral is equivalent to either of its boundedness from L1(μ)into L1,∞(μ)or from the atomic Hardy space H1(μ)into L1(μ).Moreover,we show that,if the Marcinkiewicz integral is bounded from H1(μ)into L1(μ),then it is also bounded from L∞(μ)into the space RBLO(μ)(the regularized BLO),which is a proper subset of RBMO(μ)(the regularized BMO)and,conversely,if the Marcinkiewicz integral is bounded from L∞b(μ)(the set of all L∞(μ)functions with bounded support)into the space RBMO(μ),then it is also bounded from the finite atomic Hardy space H1,∞fin(μ)into L1(μ).These results essentially improve the known results even for non-doubling measures. 相似文献
11.
We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤∞,for which the potential operators are L~p—L~q bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate L~p mapping properties of the Laplace-Stieltjes and Laplace type multipliers. 相似文献
12.
I. Ferrando 《Indagationes Mathematicae》2009,20(1):57-71
Let m be a countably additive vector measure with values in a real Banach space X, and let L1(m) and Lw(m) be the spaces of functions which are, correspondingly, integrable and weakly integrable with respect to m. Given a Young's function Φ, we consider the vector measure Orlicz spaces LΦ(m) and LΦw(m) and establish that the Banach space of multiplication operators going from W = LΦ(m) into Y = L1 (m) is M = LΨw (m) with an equivalent norm; here Ψ is the conjugated Young's function for Φ. We also prove that when W = LΦw(m), Y = L1(m) we have M = LΨw (m), and when W = LΦw(m), Y = L1(m) we have M = LΨ (m). 相似文献
13.
Zoltán Léka 《Complex Analysis and Operator Theory》2013,7(4):1321-1335
We study asymptotic properties of certain functions of the Volterra integral operator V in L p [0, 1] (1 ≤ p ≤ ∞). We also prove the Ritt property under minimal spectral assumptions for some functions of V in L 2[0, 1]. 相似文献
14.
We consider a class of Stefan-type problems having a convection term and a pseudomonotone nonlinear diffusion operator. Assuming data in L1, we prove existence, uniqueness and stability in the framework of renormalized solutions. Existence is established from compactness and monotonicity arguments which yield stability of solutions with respect to L1 convergence of the data. Uniqueness is proved through a classical L1-contraction principle, obtained by a refinement of the doubling variable technique which allows us to extend previous results to a more general class of nonlinear possibly degenerate operators. 相似文献
15.
K. Kazarian V. N. Temlyakov 《Proceedings of the Steklov Institute of Mathematics》2013,280(1):181-190
We consider a weighted L p space L p (w) with a weight function w. It is known that the Haar system H p normalized in L p is a greedy basis of L p , 1 < p < ∞. We study a question of when the Haar system H p w normalized in L p (w) is a greedy basis of L p (w), 1 < p < ∞. We prove that if w is such that H p w is a Schauder basis of L p (w), then H p w is also a greedy basis of L p (w), 1 < p < ∞. Moreover, we prove that a subsystem of the Haar system obtained by discarding finitely many elements from it is a Schauder basis in a weighted norm space L p (w); then it is a greedy basis. 相似文献
16.
We establish magnetic diffusion vanishing limit of the nonlinear pipe Magnetohydrodynamic flow by the mathematical validity of the Prandtl boundary layer theory with fixed viscosity. The convergence is verified under various Sobolev norms, including the L~∞(L~2)and L~∞(H~1) norm. 相似文献
17.
Dong Ni Tan 《数学学报(英文版)》2012,28(6):1197-1208
In this paper we study the isometric extension problem and show that every surjective isometry between the unit spheres of Lp (μ) (1 p ∞, p≠2) and a Banach space E can be extended to a linear isometry from Lp(μ) onto E, which means that if the unit sphere of E is (metrically) isometric to the unit sphere of Lp(μ), then E is linearly isometric to Lp(μ). We also prove that every surjective 1-Lipschitz or anti-1-Lipschitz map between the unit spheres of Lp (μ1, H1) and Lp(μ2,H2) must be an isometry and can be extended to a linear isometry from Lp (μ1,H1) to Lp (μ2,H2), where H1 and H2 are Hilbert spaces. 相似文献
18.
V. I. Kolyada 《Proceedings of the Steklov Institute of Mathematics》2014,284(1):192-203
We study functions of two variables whose sections by the lines parallel to the coordinate axis satisfy the Lipschitz condition of order 0 < α ≤ 1. We prove that if for a function f the Lip α-norms of these sections belong to the Lorentz space L p,1(?) (p = 1/α), then f can be modified on a set of measure zero so as to become bounded and uniformly continuous on ?2. For α = 1 this gives an extension of Sobolev’s theorem on continuity of functions of the space W 1 2,2 (?2). We show that the exterior L p,1-norm cannot be replaced by a weaker Lorentz L p,q -norm with q > 1. 相似文献
19.
We prove the following theorem:Let T be an order preserving nonexpansive operator on L 1 (μ) (or L 1 + ) of a σ-finite measure, which also decreases theL ∞-norm, and let S=tI+(1?t)T for 0<t<1. Then for everyf ∈ Lp (1<p<∞),the sequence S nf converges weakly in Lp. (The assumptions do not imply thatT is nonexpansive inL p for anyp>1, even ifμ is finite.) For the proof we show that ∥S n+1 f?S nf∥ p → 0 for everyf ∈L p, 1<p<∞, and apply toS the following theorem:Let T be order preserving and nonexpansive in L 1 + , and assume that T decreases theL ∞-norm. Then forg ∈L p (1<p<∞) Tng is weakly almost convergent. If forf ∈ Lp we have T n+1 f?T n f → 0weakly, then T nf converges weakly in Lp (1<p<∞). 相似文献
20.
Mustapha Mokhtar-Kharroubi 《Journal of Functional Analysis》2010,259(3):780-816
We deal with convolution semigroups (not necessarily symmetric) in Lp(RN) and provide a general perturbation theory of their generators by indefinite singular potentials. Such semigroups arise in the theory of Lévy processes and cover many examples such as Gaussian semigroups, α-stable semigroups, relativistic Schrödinger semigroups, etc. We give new generation theorems and Feynman-Kac formulas. In particular, by using weak compactness methods in L1, we enlarge the extended Kato class potentials used in the theory of Markov processes. In L2 setting, Dirichlet form-perturbation theory is finely related to L1-theory and the extended Kato class measures is also enlarged. Finally, various perturbation problems for subordinate semigroups are considered. 相似文献