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1.
Let T be a Calderón–Zygmund operator with regular kernel K and T * b be the maximal multilinear commutator defined by . In this paper, the following weighted estimates for T * b are discussed. Precisely, for 0 < p < ∞, ωA and b j Osc equation/tex2gif-inf-5.gif, rj ≥ 1, j = 1, … , m , there exists a positive constant C such that . For p = 1 and ωA 1, the weighted weak L (log L )1/r ‐type estimates are also established. Our theorems are parallel to the ones of the multilinear commutators of Calderón–Zygmund operators obtained in [18] and extend the main result in [14] essentially. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

2.
Let I = [a , b ] ? ?, let 1 < qp < ∞, let u and v be positive functions with uL p (I ) and vL q (I ), and let T : L p (I ) → L q (I ) be the Hardy‐type operator given by Given any n ∈ ?, let s n stand for either the n ‐th approximation number of T or the n ‐th Kolmogorov width of T . We show that where c pq is an explicit constant depending only on p and q . (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
Let X, X1, X2, … be i.i.d. random variables with nondegenerate common distribution function F, satisfying EX = 0, EX2 = 1. Let Xi and Mn = max{Xi, 1 ≤ in }. Suppose there exists constants an > 0, bnR and a nondegenrate distribution G (y) such that Then, we have almost surely, where f (x, y) denotes the bounded Lipschitz 1 function and Φ(x) is the standard normal distribution function (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

4.
We show that large positive solutions exist for the semilinear elliptic equation Δu = p(x)u α + q(x)v β on bounded domains in R n , n ≥ 3, for the superlinear case 0 < α ≤ β, β > 1, but not the sublinear case 0 < α ≤ β ≤ 1. We also show that entire large positive solutions exist for both the superlinear and sublinear cases provided the nonnegative continuous functions p and q satisfy certain decay conditions at infinity. Existence and nonexistence of entire bounded solutions are established as well.  相似文献   

5.
This paper is concerned with the existence, nonexistence, uniqueness, and non‐uniqueness of solutions for a singular parabolic equation in one dimension case. For different cases of some constant m of the equation, we study the uniqueness of solutions for m > ? 1, the nonexistence of solutions for m ≤ ? p, and the existence and non‐uniqueness of solutions for ? p < m ≤ ? 1. The novelty of this paper lies in the study of nonexistence. Moreover, the other results of this paper extend some recent works. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

6.
Let M be the classical Hardy‐Littlewood maximal operator. The object of our investigation in this paper is the iterated maximal function Mkf(x) = M(Mk?1f) (x) (k ≥ 2). Let Φ be a φ‐function which is not necessarily convex and Ψ be a Young function. Suppose that w is an A weight and that k is a positive integer. If there exist positive constants C1 and C2 such that ((I)) then there exist positive constants C3 and C4 such that ((II)) where the functions a(t) and b(t) are the right derivatives of Φ(t) and Ψ(t), respectively. Conversely, if w is an A1 weight, then (II) implies (I). Another necessary and sufficient condition will be given. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
We consider the canonical solution operator to restricted to (0, 1)‐forms with coefficients in the generalized Fock‐spaces (1) We will show that the canonical solution operator restricted to (0, 1)‐forms with ‐coefficients can be interpreted as a Hankel‐operator. Furthermore we will show that the canonical solution operator is not compact for m ≥ 2. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

8.
This paper is considering the problem of traveling wave solutions (TWS) for a susceptible-exposed-infectious-recovered (SEIR) epidemic model with discrete diffusion. The threshold condition for the existence and nonexistence of TWS is obtained. More specifically, such kind of solutions are governed by the threshold number ?0. We can find a critical wave speed c? if ?0 > 1, by employing the Schauder's fixed point theorem, limiting argument and two-sided Laplace transform, we confirm that there exists TWS for c > c?, while there exists no TWS for c < c?. We also obtain the nonexistence of TWS for ?0 ≤ 1. At last, we give some biological explanations from the epidemiological perspective.  相似文献   

9.
In this article, for the symmetric pendulum equation and the symmetric bisuperlinear equation respectively, we show that there are two one-parameter families of solutions, ys and ya, so that one is adiabatically symmetric, ys(?t)=ys(t)+ok) for all k≥0, and the other adiabatically antisymmetric, ya(?t)=?ya(t)+ok) for all k≥0. By using the techniques of exponential asymptotics to calculate ys(0) and ya(0), we demonstrate that, in general, they are not genuinely symmetric or antisymmetric, because these quantities are in fact exponentially small. Finally, after establishing a relationship between the total change in the leading-order adiabatic invariant and the quantity ys(0) for the family of solutions ys of the bisuperlinear equation, we are able to reveal explicitly how the behavior of the adiabatic invariant depends on the complex singularities of the equation.   相似文献   

10.
In this paper we deal with boundary value problems where l : C1([a, b], ?k) → ?k × ?k is continuous, μ ≤ 0 and φ is a Caratheodory map. We define the class S of maps l, for which a global bifurcation theorem holds for the problem (+), with φ(t, x, y, λ) = λ(|x1|, …, |xk|) + o(|x| + |y|). We show that the class S contains Sturm‐Liouville boundary conditions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

11.
We consider an important class of subnormal operator m-tuples M p (p = m,m + 1, . . .) that is associated with a class of reproducing kernel Hilbert spaces Hp{{\mathcal H}_p} (with M m being the multiplication tuple on the Hardy space of the open unit ball \mathbb B2m{{\mathbb B}^{2m}} in \mathbb Cm{{\mathbb C}^m} and M m+1 being the multiplication tuple on the Bergman space of \mathbb B2m{{\mathbb B}^{2m}}). Given any two C*-algebras A{\mathcal A} and B{\mathcal B} from the collection {C*(Mp), C*([(M)\tilde]p): p 3 m}{\{C^*({M}_p), C^*({\tilde M}_p): p \geq m\}} , where C*(M p ) is the unital C*-algebra generated by M p and C*([(M)\tilde]p){C^*({\tilde M}_p)} the unital C*-algebra generated by the dual [(M)\tilde]p{{\tilde M}_p} of M p , we verify that A{\mathcal A} and B{\mathcal B} are either *-isomorphic or that there is no homotopy equivalence between A{\mathcal A} and B{\mathcal B} . For example, while C*(M m ) and C*(M m+1) are well-known to be *-isomorphic, we find that C*([(M)\tilde]m){C^*({\tilde M}_m)} and C*([(M)\tilde]m+1){C^*({\tilde M}_{m+1})} are not even homotopy equivalent; on the other hand, C*(M m ) and C*([(M)\tilde]m){C^*({\tilde M}_{m})} are indeed *-isomorphic. Our arguments rely on the BDF-theory and K-theory.  相似文献   

12.
It is well known that if m is an L p -multiplier for the Fourier transform on \mathbbRn{\mathbb{R}^n} , (1 < p < ∞) then there exists a pseudomeasure σ such that T m fσ * f . A similar problem is discussed for the L p −Fourier multipliers for H{\mathcal{H}} -valued functions on the Heisenberg group, where H{\mathcal{H}} is a separable Hilbert space.  相似文献   

13.
J. Lindenstrauss proves in [L] thatc 0(Γ) is not quasicomplemented inl (Γ) while H. P. Rosenthal in [R] proves that subspaces, whose dual balls are weak* sequentially compact and weak* separable, are quasicomplemented inl (Γ). In this note it is proved that weak* separability of the dual is the precise condition determining whether a subspace, without isomorphic copies ofl 1 and whose dual balls are weak* sequentially compact, is quasicomplemented or not inl (Γ). Especially spaces isomorphic tol p(Γ), for 1<p<∞, have no quasicomplements inl (Γ) if Γ is uncountable.  相似文献   

14.
In this paper, the existence and nonexistence of finite travelling waves (FTWs) for a semilinear degenerate reaction-diffusion system is studied, where 0 < α i < 1, m ij ≥ 0 and ∑ N j =1 m ij > 0, i, j = 1,...,N. Necessary and sufficient conditions on existence and large time behaviours of FTWs of (I) are obtained by using the matrix theory, Schauder's fixed point theorem, and upper and lower solutions method. Received July 3, 1997, Revised June 23, 1999, Accepted March 29, 2000  相似文献   

15.
The possible continuation of solutions of the nonlinear heat equation in RN × R+ ut = Δum + up with m > 0, p > 1, after the blowup time is studied and the different continuation modes are discussed in terms of the exponents m and p. Thus, for m + p ≤ 2 we find a phenomenon of nontrivial continuation where the region {x : u(x, t) = ∞} is bounded and propagates with finite speed. This we call incomplete blowup. For N ≥ 3 and p > m(N + 2)/(N − 2) we find solutions that blow up at finite t = T and then become bounded again for t > T. Otherwise, we find that blowup is complete for a wide class of initial data. In the analysis of the behavior for large p, a list of critical exponents appears whose role is described. We also discuss a number of related problems and equations. We apply the same technique of analysis to the problem of continuation after the onset of extinction, for example, for the equation ut = Δum − up, m > 0. We find that no continuation exists if p + m ≤ 0 (complete extinction), and there exists a nontrivial continuation if p + m > 0 (incomplete extinction). © 1997 John Wiley & Sons, Inc.  相似文献   

16.
We consider the approximation of periodic functions by trigonometric polynomials in metric (not normed) spaces that are generalizations of the spaces L p , 0 < p < 1, and L 0. In particular, we prove the multidimensional Jackson theorem in L p (T m ), 0 < p < 1.  相似文献   

17.
Denote by πn the set of all algebraic polynomials of degree at most n with complex coefficients. An inequality of I. Schur asserts that the first derivative of the transformed Tchebycheff polynomial has the greatest uniform norm in [?1, 1] among all f ∈ ??n, where (1) Here we show that this extremal property of persists in the wider class of polynomials f ∈ πn which vanish at ±1, and for which there exist n ? 1 points separating the zeros of and such that for j = 1, …, n ? 1. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

18.
In this paper we calculate which prime powers ps divide Δn, m = g.c.d.{k! S(n, k)|mkn} for s < p. Here S(n, k) is a Stirling number of the second kind.  相似文献   

19.
The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div([↓△u^m|p-2↓△u^m). It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 + 1/m and will be positive for p 〉 1 + 1/m for large t, where m 〉 0.  相似文献   

20.
It is shown that if X is an n – dimensional subspace of Lp, 0 < p < 1, then there exists a subspace Y of 𝓁Np such that d(X, Y) ≤ 1 + ε and NC(ε, p)n(log n)3.  相似文献   

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