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1.
  相似文献   

2.
Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,
｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.
The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.  相似文献   

3.
We are going to discuss special cases of a conditional functional inequality
whereX is a real inner product space. In particular, we will give conditions which force the representationf(x)=c‖x‖2+a(x) for x ∈X, where c ∈ R anda:x→ℝ is an additive functional.  相似文献   

4.
We study the weak* lower semicontinuity properties of functionals of the form
where Ω is a bounded open set of R N and u∈W 1,∞(Ω). Without a continuity assumption on f(⋅,ξ) we show that the supremal functional F is weakly* lower semicontinuous if and only if it is a level convex functional (i.e. it has convex sub-levels). In particular if F is weakly* lower semicontinuous, then it can be represented through a level convex function. Finally a counterexample shows that in general it is not possible to represent F through the level convex envelope of f.  相似文献   

5.
Let Sk(Γ) be the space of holomorphic Γ-cusp forms f(z) of even weight k ≥ 12 for Γ = SL(2, ℤ), and let Sk(Γ)+ be the set of all Hecke eigenforms from this space with the first Fourier coefficient af(1) = 1. For f ∈ Sk(Γ)+, consider the Hecke L-function L(s, f). Let
It is proved that for large K,
where ε > 0 is arbitrary. For f ∈ Sk(Γ)+, let L(s, sym 2 f) denote the symmetric square L-function. It is proved that as k → ∞ the frequence
converges to a distribution function G(x) at every point of continuity of the latter, and for the corresponding characteristic function an explicit expression is obtained. Bibliography: 17 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 221–246.  相似文献   

6.
LetD ⊂C N ,N ≥ 2 be a bounded open set withC 2 boundary and letL be an open connected set of affine complex hyperplanes inC N containing a hyperplane that misses . LetE = ∪Λ∈LΛ, Γ =E ∩bD. Suppose thatf ∈C(Γ) and assume that
  相似文献   

7.
This paper deals with the existence of weak solutions in W 01(Ω) to a class of elliptic problems of the form
in a bounded domain Ω of ℝ N . Here a satisfies
for all ξ∈ℝ N , a.e. x∈Ω, , h 1∈L loc 1(Ω), h 1(x)≧1 for a.e. x in Ω; λ 1 is the first eigenvalue for −Δ p on Ω with zero Dirichlet boundary condition and g, h satisfy some suitable conditions.   相似文献   

8.
Let f(x, y) be a periodic function defined on the region D
with period 2π for each variable. If f(x, y) ∈ C p (D), i.e., f(x, y) has continuous partial derivatives of order p on D, then we denote by ω α,β(ρ) the modulus of continuity of the function
and write
For p = 0, we write simply C(D) and ω(ρ) instead of C 0(D) and ω 0(ρ). Let T(x,y) be a trigonometrical polynomial written in the complex form
We consider R = max(m 2 + n 2)1/2 as the degree of T(x, y), and write T R(x, y) for the trigonometrical polynomial of degree ⩾ R. Our main purpose is to find the trigonometrical polynomial T R(x, y) for a given f(x, y) of a certain class of functions such that
attains the same order of accuracy as the best approximation of f(x, y). Let the Fourier series of f(x, y) ∈ C(D) be
and let
Our results are as follows Theorem 1 Let f(x, y) ∈ C p(D (p = 0, 1) and
Then
holds uniformly on D. If we consider the circular mean of the Riesz sum S R δ (x, y) ≡ S R δ (x, y; f):
then we have the following Theorem 2 If f(x, y) ∈ C p (D) and ω p(ρ) = O(ρ α (0 < α ⩾ 1; p = 0, 1), then
holds uniformly on D, where λ 0 is a positive root of the Bessel function J 0(x) It should be noted that either
or
implies that f(x, y) ≡ const. Now we consider the following trigonometrical polynomial
Then we have Theorem 3 If f(x, y) ∈ C p(D), then uniformly on D,
Theorems 1 and 2 include the results of Chandrasekharan and Minakshisundarm, and Theorem 3 is a generalization of a theorem of Zygmund, which can be extended to the multiple case as follows Theorem 3′ Let f(x 1, ..., x n) ≡ f(P) ∈ C p and let
where
and
being the Fourier coefficients of f(P). Then
holds uniformly. __________ Translated from Acta Scientiarum Naturalium Universitatis Pekinensis, 1956, (4): 411–428 by PENG Lizhong.  相似文献   

9.
The following regularity of weak solutions of a class of elliptic equations of the form are investigated.  相似文献   

10.
Global attractivity in a discrete delay logistic model   总被引：1，自引：0，他引：1  
1.IntroductionIntherecentworks[l--31,theauthorsconsideredthediscretedelaylogisticmodelIn[3],itwasshownthateverypositivesolutionof(l)oscillatesaboutitspositiveequilibriumx~(a--1)/0ifandonlyifIn[if(seealso[2]),itwasprovedthatiftheneverypositivesolutionof(1)tendstox~(or--1)/pasn-- co.Thepurposeofthispaperistoobtainanothersufficieatconditionforthepositiveequilibriumxof(1)tobeaglobalattractorbyusingamethodverydmerelltfromthatusedin[1,21.Themainresultofthispaperisthefollowingtheorem.*Thisworkispart…  相似文献   

11.
For functions satisfying the boundary conditions
, the following inequality with sharp constants in additive form is proved:
wheren≥2, 0≤1≤n−2,−1≤m≤1, m+1≤n−3, and1≤p,q,r≤∞. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 712–724, November, 1997. Translated by N. K. Kulman  相似文献   

12.
Lewin 《Semigroup Forum》2008,66(1):43-62
   Abstract. Given a set A and a function
, we study the set of all functions
that are continuous for all topologies for which f continuous. We prove that in a sense to be made precise in the text, for any essentially infinitary function f , any non-constant such g equals f n , for some n∈ N. We also prove a similar result for the clone of n -ary functions from
.  相似文献   

13.
Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem
where ω  >  0, ℓi : C([0, ω])→ L([0,ω]) are linear bounded operators, and qi∈L([0, ω]). Received: 11 June 2005  相似文献   

14.
Let Γ be a smooth compact convex planar curve with arc length dm and let dσ=ψ dm where ψ is a cutoff function. For Θ∈SO (2) set σΘ(E) = σ(ΘE) for any measurable planar set E. Then, for suitable functions f in ℝ2, the inequality.
represents an average over rotations, of the Stein-Tomas restriction phenomenon. We obtain best possible indices for the above inequality when Γ is any convex curve and under various geometric assumptions.  相似文献   

15.
In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation
（φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1,
subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r） 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.  相似文献   

16.
Let Ω be a bounded open subset of ℝ n , n > 2. In Ω we deduce the global differentiability result
for the solutions u ∈ H 1 (Ω, ℝ n ) of the Dirichlet problem
with controlled growth and nonlinearity q = 2. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.  相似文献   

17.
Let ℋ be a separable infinite dimensional complex Hilbert space, and let ℒ(H) denote the algebra of all bounded linear operators on ℋ into itself. Let A = (A 1, A 2,..., A n), B = (B 1, B 2,..., B n) be n-tuples of operators in ℒ(H); we define the elementary operators Δ A,B : ℒ(H) ↦ ℒ(H) by
. In this paper, we characterize the class of pairs of operators A, B ∈ ℒ(H) satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators A,B ∈ ℒ(H) such that implies for all T ∈ C 1 (H) (trace class operators). The main result is the equivalence between this property and the fact that the ultraweak closure of the range of the elementary operator ΔA,B is closed under taking adjoints. This leads us to give a new characterization of the orthogonality (in the sense of Birkhoff) of the range of an elementary operator and its kernel in C 1 classes. This work was supported by the research center project No. 2005-04.  相似文献   

18.
§１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｐｅｒ,ｗｅｃｏｎｓｉｄｅｒｔｈｅｉｎｉｔｉａｌａｎｄｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍａｓｆｏｌｏｗｓ：ｕｔ＝Δ（ｇｒａｄφ（ｕ））＋αΔｂ（ｕ）＋ｆ（ｘ,ｔ,ｕ）,（ｘ,ｔ）∈ＱＴ＝Ω×（０,Ｔ］（...  相似文献   

19.
In this paper, the existence of unbounded solutions for the following nonlinear asymmetric oscillator
is discussed, where α, β are positive constants satisfying
for some ω ∈R+ /Q, h(t) ∈L∞ [0, 2π ] is 2π-periodic, x±=max {±x, 0 }. Received: 23 September 2004  相似文献   

20.
Let f be an analytic function in a complex domain D and (without loss of generality) assume 0∈D. Then the paper’s aim is to derive a Taylor-like integral expression for f, i.e. an integral representation analogous to the corresponding power series, say, ∑ k=0∞ a k t k /k!. We start from the simplest case f(t)=e t , which leads to the identity
valid for Re  t>0, Γ denoting the Euler gamma function. This statement turns out as the result of a summation of the divergent integral ∫ −∞∞ t y /Γ(y+1)dy, so that, in the sense of summability, the formula
holds, i.e. a perfect integral analogue of the corresponding series. Next, we consider the important case of polynomial, resp. monomial f. Then we will apply our statements (on polynomials) to the general case of any function f analytic at 0. Particularly, we will deduce some remarkable statements about the function log (1+x) and its powers, i.e. on the Stirling numbers of the first kind and their generalization to C, the so-called Butzer-Stirling functions. Finally we present a general method for deriving results for large classes of other functions. Dedicated to Prof. Dr. Paul L. Butzer, Aachen.  相似文献   

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