共查询到20条相似文献,搜索用时 31 毫秒
1.
Ismail Kombe 《Mathematische Nachrichten》2006,279(7):756-773
In this paper, we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equations: and Here, Ω is a Carnot–Carathéodory metric ball in R N and V ∈ L 1loc(Ω). The critical exponents m * and p * are found, and the nonexistence results are proved for m * ≤ m < 1 and p * ≤ p < 2. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Pu Zhang 《Mathematische Nachrichten》2006,279(4):445-462
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 < ∞, ω ∈ A ∞ 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 ω ∈ A 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
3.
In this paper, we study the existence of anti‐periodic solutions for the first order evolution equation in a Hilbert space H, where G : H → ? is an even function such that ?G is a mapping of class (S+) and f : ? → ? satisfies f(t + T) = –f(t) for any t ∈ ? with f(·) ∈ L2(0, T; H). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
Meirong Zhang 《Mathematische Nachrichten》2005,278(15):1823-1836
Given a positive integer n and an exponent 1 ≤ α ≤ ∞. We will find explicitly the optimal bound rn such that if the Lα norm of a potential q (t ) satisfies ‖q ‖equation/tex2gif-inf-2.gif < rn then the n th Dirichlet eigenvalue of the onedimensional p ‐Laplacian with the potential q (t ): (|u ′|p –2 u ′)′ + (λ + q (t )) |u |p –2u = 0 (1 < p < ∞) will be positive. Using these bounds, we will construct, for the Dirichlet, the Neumann, the periodic or the antiperiodic boundary conditions, certain classes of potentials q (t ) so that the p ‐Laplacian with the potential q (t ) is non‐degenerate, which means that the above equation with λ = 0 has only the trivial solution verifying the corresponding boundary condition. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Rieko Shimada 《Mathematical Methods in the Applied Sciences》2007,30(3):257-289
We obtain the Lp–Lq maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ?n (n?2). The Robin condition consists of two conditions: v ? u=0 and αu+β(T(u, p)v – 〈T(u, p)v, v〉v)=h on the boundary of the domain with α, β?0 and α+β=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and non‐slip one when α=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
6.
Let I=[a,b]⊂R, let 1<p?q<∞, let u and v be positive functions with u∈Lp′(I), v∈Lq(I) and let be the Hardy-type operator given by
7.
Teresa Martínez 《Mathematische Nachrichten》2003,251(1):52-63
For 1 < p < ∞, the almost surely finiteness of is a necessary and sufficient condition in order to have almost surely convergence of the sequences {E(f|?n)} with f ∈ Lp(v dP). This condition is also equivalent to have weighted inequalities from Lp(v dP) into Lp(u dP) for some weight u for Doob's maximal function, square function and generalized Burkholder martingale transforms. Similarly, E(u|?1) < ∞ turns out to be necessary and sufficient for the above weighted inequalities to hold for some v. 相似文献
8.
We consider the following type of problems. Given a graph G = (V, E) and lists L(v) of allowed colors for its vertices v ∈ V such that |L(v)| = p for all v ∈ V and |L(u) ∩ L(v)| ≤ c for all uv ∈ E, is it possible to find a “list coloring,” i.e., a color f(v) ∈ L(v) for each v ∈ V, so that f(u) ≠ f(v) for all uv ∈ E? We prove that every of maximum degree Δ admits a list coloring for every such list assignment, provided p ≥ . Apart from a multiplicative constant, the result is tight, as lists of length may be necessary. Moreover, for G = Kn (the complete graph on n vertices) and c = 1 (i.e., almost disjoint lists), the smallest value of p is shown to have asymptotics (1 + o(1)) . For planar graphs and c = 1, lists of length 4 suffice. ˜© 1998 John Wiley & Sons, Inc. J Graph Theory 27: 43–49, 1998 相似文献
9.
Let u =(uh, u3) be a smooth solution of the 3-D Navier-Stokes equations in R3× [0, T). It was proved that if u3 ∈ L∞(0, T;˙B-1+3/p p,q(R3)) for 3 p, q ∞ and uh∈ L∞(0, T; BMO-1(R3)) with uh(T) ∈ VMO-1(R3), then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al.(2016), which requires u ∈ L∞(0, T;˙B-1+3/pp,q(R3)). Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest. 相似文献
10.
Letf ∈L p (I) and denote byB n,p (f) the polynomial of bestL p-approximation tof of degreen (1<p<∞,I=[?1,1], the norm is weightedL p-norm with an arbitrary positive weight). Extending a result proved by Saff and Shekhtman forp=2 we show that for every 1<p<∞ andf ∈L p (I) (not a polynomial) points of sign change of the error functionf-B n,p (f) are dense inI asn→∞. 相似文献
11.
For 0 < p < 1 and q > 0 let Gq(n,p) denote the random graph with vertex set [n]={1,…,n} such that, for each graph G on [n] with e(G) edges and c(G) components, the probability that Gq(n,p)=G is proportional to . The first systematic study of Gq(n,p) was undertaken by 6 , who analyzed the phase transition phenomenon corresponding to the emergence of the giant component. In this paper we describe the structure of Gq(n,p) very close the critical threshold. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 相似文献
12.
Let Δ(x) = max {1 - ¦x¦, 0} for all x ∈ ?, and let ξ[0,1) be the characteristic function of the interval 0 ≤x < 1. Two seminal theorems of M. Jodeit assert that A and ξ[0,1) act as summability kernels convertingp-multipliers for Fourier series to multipliers forL P (?). The summability process corresponding to Δ extendsL P (T)-multipliers from ? to ? by linearity over the intervals [n, n + 1],n ∈ ?, when 1 ≤p < ∞, while the summability process corresponding to ξ[0,1) extends LP(T)-multipliers by constancy on the intervals [n, n + 1),n ∈ ?, when 1 <p < ∞. We describe how both these results have the following complete generalization: for 1 ≤p < ∞, an arbitrary compactly supported multiplier forL P (?) will act as a summability kernel forL P (T)-multipliers, transferring maximal estimates from LP(T) to LP(?). In particular, specialization of this maximal theorem to Jodeit’s summability kernel ξ[0, 1) provides a quick structural way to recover the fact that the maximal partial sum operator on LP(?), 1 <p < ∞, inherits strong type (p,p)-boundedness from the Carleson-Hunt Theorem for Fourier series. Another result of Jodeit treats summability kernels lacking compact support, and we show that this aspect of multiplier theory sets up a lively interplay with entire functions of exponential type and sampling methods for band limited distributions. 相似文献
13.
In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (H
p,q
(φ1), H
u,v
(φ2)) for the values of p, q, u, v in three cases: (i) 0 < p ≤ u ≤ ∞, 0 < q ≤ min(1, v) ≤ ∞. (ii) v = ∞, 0 < p ≤ u ≤ ∞, 1 ≤ u, q ≤ ∞. (iii) 1 ≤ v ≤ 2 ≤ q ≤ ∞, and 0 < p ≤ u ≤ ∞ or 1 ≤ p, u ≤ ∞. The first case extends the result of Blasco, Jevtić, and Pavlović in one variable. The third case generalizes partly
the results of Jevtić, Jovanović, and Wojtaszczyk to higher dimensions.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
14.
Kazushi Yoshitomi 《Indagationes Mathematicae》2005,16(2):289-299
Let q ∈ {2, 3} and let 0 = s0 < s1 < … < sq = T be integers. For m, n ∈ Z, we put ¯m,n = {j ∈ Z| m? j ? n}. We set lj = sj − sj−1 for j ∈ 1, q. Given (p1,, pq) ∈ Rq, let b: Z → R be a periodic function of period T such that b(·) = pj on sj−1 + 1, sj for each j ∈ 1, q. We study the spectral gaps of the Jacobi operator (Ju)(n) = u(n + 1) + u(n − 1) + b(n)u(n) acting on l2(Z). By [λ2j , λ2j−1] we denote the jth band of the spectrum of J counted from above for j ∈ 1, T. Suppose that pm ≠ pn for m ≠ n. We prove that the statements (i) and (ii) below are equivalent for λ ∈ R and i ∈ 1, T − 1. 相似文献
15.
José María Martell 《Journal of Mathematical Analysis and Applications》2004,294(1):223-236
We prove two-weight, weak type norm inequalities for potential operators and fractional integrals defined on spaces of homogeneous type. We show that the operators in question are bounded from Lp(v) to Lq,∞(u), 1<p?q<∞, provided the pair of weights (u,v) verifies a Muckenhoupt condition with a “power-bump” on the weight u. 相似文献
16.
Lahcne Mezrag 《Mathematische Nachrichten》2004,266(1):60-67
In [5], it is proved that a bounded linear operator u, from a Banach space Y into an Lp(S, ν) factors through Lp1 (S, ν) for some p1 > 1, if Y* is of finite cotype; (S, ν) is a probability space for p = 0, and any measure space for 0 < p < 1. In this paper, we generalize this result to uv, where u : Y → Lp(S, ν) and v : X → Y are linear operators such that v* is of finite Ka?in cotype. This result gives also a new proof of Grothendieck's theorem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Higher order commutators for a class of rough operators 总被引:12,自引:0,他引:12
In this paper we study the (L
p
(u
p
),L
q
(v
q
)) boundedness of the higher order commutatorsT
Ω,α,b
m
andM
Ω,α,b
m
formed by the fractional integral operatorT
Ω,α
, the fractional maximal operatorM
Ω,α
, and a functionb(x) in BMO(v), respectively.
Our results imporve and extend the corresponding results obtained by Segovia and Torrea in 1993 [9].
The project was supported by NNSF of China. 相似文献
18.
Yasushi Taniuchi 《manuscripta mathematica》1997,94(1):365-384
We show that for every initial dataa εL
2(Ω) there exists a weak solutionu of the Navier-Stokes equations satisfying the generalized energy inequality introduced by Caffarelli-Kohn-Nirenberg forn=3. We also show that if a weak solutionu εL
s
(0,T;L
q
(Ω)) with 2/q + 2/s ≤ 1 and 3/q + 1/s ≤ 1 forn=3, or 2/q + 2/s ≤ 1 andq ≥ 4 forn ≥ 4, thenu satisfies both the generalized and the usual energy equalities. Moreover we show that the generalized energy equality holds
only under the local hypothesis thatu εL
s
(ε, T; L
q
(K)) for all compact setsK ⊂ ⊂ Ω and all 0 <ε <T with the same (q, s) as above when 3 ≤n ≤ 10. 相似文献
19.
Y. Rakotondratsimba 《Georgian Mathematical Journal》1998,5(2):177-200
Conditions on weightsu(·),v(·) are given so that a classical operatorT sends the weighted Lorentz spaceL
Lrs
(vdx) intoL
pq
(udx). HereT is either a fractional maximal operatorM
α
or a fractional integral operatorI
α
or a Calderón-Zygmund operator. A characterization of this boundedness is obtained forM
α
andI
α
when the weights have some usual properties and max(r, s) ≤ min(p, q). 相似文献
20.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献