共查询到20条相似文献，搜索用时 62 毫秒
2.
Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi＞0,m∑I=1βi=β,0＜β＜1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn). 相似文献
3.
Some new oscillation criteria for nonlinear delay difference equation with damping △^2xn＋pn△xn＋F（n,x（n-τ,△x（n-σ）=0,n=0,1,2,…,（＊）are given. Our results partially solve the open problem posed in [Math. Bohemica, 125 （2000）, 421- 430]. Also, we will establish some new oscillation criteria for special cases of （＊）, which improve some of the well-known results in the literature. 相似文献
4.
We obtain new exact inequalities of the form for functions defined on the axis R or the semiaxis R
+ in the case where for functions defined on the axis R in the case where and for functions of constant sign on R or R
+ in the case where and in the case where .
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 291–302, March, 2006. 相似文献
5.
In this paper we introduce a new type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds.
We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case
of equi-Gaussian curvature foldings, f: M → P
n
, of an orientable surface M onto a polygon P
n
we prove that
and we generalize (iii) for # nT
2. 相似文献
6.
In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian
and
are studied and some new multiplicity results of solutions for systems (1.λ) and (2.λ) are obtained. Moreover, by using the
KKM principle we give also two new existence results of solutions for systems (1.1) and (2.1).
This Work is supported in part by the National Natural Science Foundation of China (10561011). 相似文献
7.
In this paper, we prove that each sufficiently large integer N ≠1（mod 3） can be written as N=p＋p1^2＋p2^2＋p3^2＋p4^2, with ｜p-N/5｜≤U,｜pj-√N/5｜≤U,j=1,2,3,4, where U=N^2/20＋c and p,pj are primes. 相似文献
8.
Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1 01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(… 相似文献
9.
For positive integers with a
r
= 2, the multiple zeta value or r-fold Euler sum is defined as [2]
. There is a celebrated sum formula [6, 10] among multiple zeta values as ,
where range over all positive integers with in the summation.
In this paper, we shall prove the so called restricted sum formula [4]. Namely, for all positive integers m and q with m ≥ q and a nonnegative integer p, that
. We prove the assertion by new expressions of multiple zeta values in terms of Drinfeld integrals.
This work was supported by the Department of Mathematics, National Chung Cheng University and by the National Science Council
of Taiwan, Republic of China. 相似文献
10.
We study the limit as n goes to +∞ of the renormalized solutions u
n
to the nonlinear elliptic problems
where Ω is a bounded open set of ℝ
N
, N≥ 2, and μ is a Radon measure with bounded variation in Ω. Under the assumption of G-convergence of the operators , defined for , to the operator , we shall prove that the sequence ( u
n
) admits a subsequence converging almost everywhere in Ω to a function u which is a renormalized solution to the problem
相似文献
11.
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
12.
Let D be an increasing sequence of positive integers, and consider the divisor functions：
d（n, D） =∑d｜n,d∈D,d≤√n1, d2（n,D）=∑[d,δ]｜n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.（d,δ）. A probabilistic argument is introduced to evaluate the series ∑n=1^∞and（n,D） and ∑n=1^∞and2（n,D）. 相似文献
13.
The following boundary value problem is studied: here the surface Г satisfies the condition(
, where and ν is the outward (with respect to Ω) normal to Γ.
Translated from Matematischskie Zametki, Vol. 61, No. 5, pp. 759–768, May, 1997.
Translated by N. K. Kulman 相似文献
14.
We obtain sufficient conditions for the Perron stability of the trivial solution of a real difference equation of the form where and. The resuits obtained are valid for the case where.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 12, pp. 1593–1603, December, 1999. 相似文献
15.
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which
（i） lim sup n→∞ ｜｜Sn｜｜/an〈∞ a.s.and
∞ ∑n=1（1/n）P（｜｜Sn｜｜/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞） are equivalent;
（ii） For all constants λ ∈ [0, ∞）,
lim sup ｜｜Sn｜｜/an =λ a.s.and ^∞∑ n=1（1/n） P（｜｜Sn｜｜/an ≥ε）{〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables. 相似文献
16.
We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations and with the infinite-dimensional Laplacian Δ L. 相似文献
17.
In 1939 Agnew presented a series of conditions that characterized the oscillation of ordinary sequences using ordinary square
conservative matrices and square multiplicative matrices. The goal of this paper is to present multidimensional analogues
of Agnew’s results. To accomplish this goal we begin by presenting a notion for double oscillating sequences. Using this notion
along with square RH-conservative matrices and square RH-multiplicative matrices, we will present a series of characterization
of this sequence space, i.e. we will present several necessary and sufficient conditions that assure us that a square RH-multiplicative(square
RH-conservative) be such that for each double real bounded sequences { s
k;l
} where In addition, other implications and variations are also presented.
相似文献
18.
§ 1 ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｄｅｌａｙｌｏｇｉｓｔｉｃｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｙｎ =ｐｎｙｎ( 1 - ｙτ(ｎ) ) ,ｎ =0 ,1 ,2 ,...,( 1 1 )ｗｈｅｒｅｐｎ ∞ｎ =0 ｉｓａｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒｅａｌｎｕｍｂｅｒｓ ,τ(ｎ) ∞ｎ =0 ｉｓａｎｏｎｄｅｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｉｎｔｅｇｅｒｓ,τ(ｎ) <ｎａｎｄｌｉｍｎ→∞τ(ｎ) =∞ ,Δｙｎ=ｙｎ +1- ｙｎ.Ｍｏｔｉｖａｔｅｄｂｙｐｌａｕｓｉｂｌｅａｐｐｌｉｃａｔｉｏｎｓ… 相似文献
19.
Let
be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [ a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators
generated by a multiplier matrix
defined by the following relations: and In the case || = || = 1/2, we prove the following statements for the Jacobi polynomials (these statements are similar to known results for the trigonometrical system). Consider the cases
and Under some conditions on a function , the values
and
equal and In addition, we show that for the Fourier–Legendre summation methods ( = = 0) generated by the multiplier function
, the limit and supremum of the sequence of Lebesgue constants may differ. Bibliography: 11 titles. 相似文献
|
