GENERALIZED HILBERT OPERATOR AND FEJR-RIESZ TYPE INEQUALITIES ON THE POLYDISC

Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type inequalit...     

APPROXIMATION BY WALSH-KACZMARZ-FEJR MEANS ON THE HARDY SPACE

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fejr means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0 p ≤ 1/2.     

APPROXIMATION BY WALSH-KACZMARZ-FEJ ′ER MEANS ON THE HARDY SPACE

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.     

A NOTE ON MARCINKIEWICZ INTEGRALS WITH H^1 KERNELS

This paper shows that for Ω∈ H1(Sn-1), Marcinkiewicz integral operator μΩ is Lp(Rn) bounded for 1 < p <∞, which improves some known results.     

Decomposition of $L^{p}(\partial D_{a})$ Space and Boundary Value of Holomorphic Functions

This paper deals with two topics mentioned in the title.First,it is proved that function f in Lp((O)Da) can be decomposed into a sum g + h,where Da is an angular domain in the complex plane,g and h are the non-tangential limits of functions in Hp(Da) and Hp((D)cn) in the sense of Lp(Da),respectively.Second,the sufficient and necessary conditions between boundary values of holomorphic functions and distributions in n-dimensional complex space are obtained.     

A NOTE ON THE C.NEUMANN PROBLEM

We prove that the C. Neumann problem in the case where the potential matrix A hasmultiple eigenvalues is completely integrable by means of the moment map and the confocalquadric.     

A NOTE ON THE CHARACTERISTICS OF POISSON PROCESSES

In this note two characteristic theorems of Poisson processes are given.If{N(t);t≥0}is arenewal process,U_t,V_t are,respectively,the time since the last renewal and the time to the nextrenewal at t,Z_t=U_t+V_t,then a Poisson process can be characterized by the limiting independenceof the joint distribution of(U_t,V_t)when t→∞,or EZ_t,or the distribution of Z_t.     

A NOTE ON THE GENERALIZED RIEMANN PROBLEM~*

§ 1. Introduction The Riemann problem for the quasilinear hyperbolic system of conservation laws     

A NOTE ON THE NUMBER OF CUBIC PLANAR MAPS

This note shows that the number of rooted cubic planar maps (loops and multi-edges are allowed) with 2n-3 non-root-vertices, n≥3, is     

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES＊

Using a fixed-point method,we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation:f(kx + y) + f(kx - y) =kf(x + y) + kf(x -y) + 2f(kx) - 2kf(x) in Banach modules o...     

A NOTE TO OSCILLATORY SINGULAR INTEGRALS ON HERZ—TYPE SPACES

In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Hertz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebrasin higher dimensions.     

Dirichlet函数类的Fejér算子逼近

对Cn中的单位球Bn上的Dirichlet类Dp,得到与Hardy空间Hp的包含关系,并获得其精确的多项式逼近阶和以Hardy空间度量的Fejér算子逼近的一个上界估计.     

A NOTE ON A PROBLEM OF BOAS R.P.

To answer the rest part of the problem of Boas R. P. on derivative of poiyaomial, it is shown that if p(s) is a polynomial of degree n such that ■|p(z)|≤1 and. p(s)≠0 in |z|≤k, 0相似文献   

A NOTE ON RECURRENT SETS

ＡＮＯＴＥＯＮＲＥＣＵＲＲＥＮＴＳＥＴＳ￥ＷＥＮＺＨＩＹＩＮＧ；ＷＵＬＩＭＩＮＧ；ＺＨＯＮＧＨＯＮＧＬＩＵ（ＤｅｐａｒｔｍｅＤｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙｓＷｕｈａｎ４３００７２，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｔｈｅ...     

A NOTE ON A TRANSFERENCE THEOREM OF THE SYSTEMS OF LINEAR CONGRUENCES

<正> Let p be a prime number. Let a_(ij)(1≤i≤t,1≤j≤s) be a set of st integers.Weuse the notations x=max(1, |x|), p_1=[(p-1)/2], p_2=[p/2], and (a)_p to denote the integer satisfying (a)_p=a(mod p),-p_1≤(a)_p≤p_2. Consider the dual of linear congruences     

A NOTE ON THE GLOBAL SOLUTIONS OF A SEMILINEAR REACTION DIFFUSION SYSTEM

ＡＮＯＴＥＯＮＴＨＥＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＯＦＡＳＥＭＩＬＩＮＥＡＲＲＥＡＣＴＩＯＮＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭ（王明新，吴永辉）￥ＷａｎｇＭｉｎｇｘｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓＭｅｃｈａｎｉｃｓ，ＳｏｕｔｈｅａｓｔＵｎｉｖ，...     

Variable Exponent Herz Type Hardy Spaces and Their Applications

In this paper,the authors introduce certain Herz type Hardy spaces with variable exponents and establish the characterizations of these spaces in terms of atomic and molecular decompositions. Using these decompositions,the authors obtain the boundedness of some singular integral operators on the Herz type Hardy spaces with variable exponents.     

Function characterizations via commutators of Hardy operator

This paper is a summary of the research on the characterizations of central function spaces by the author and his collaborators in the past ten years.More precisely,the author gives some characterizations of central Campanato spaces via the boundedness and compactness of commutators of Hardy operator.     

A NOTE ON THE ONSET OF MELTING IN A CLASS OF SIMPLE METALS CONDITION ON THE APPLIED BOUNDARY FLUX

The onset of melting in a class of simple metals is considered for an applied heat flux q_0=h_0/t~(1/2) at the boundary. Reduction of the nonlinear problem to a linear canonical form is obtained by a reciprocal transformation. Bounds are obtained on h_0 for melting to occur.     

A NOTE ON A COVERING LEMMA OF A CORDOBA AND R FEFFERMAN~(**)

This note simplifies Cordoba-Fefferman's proof on the weak boundedness of strong maximal operator M_8 (with respect to dμ) on L(1+log~(+(n-1))L). Some two-weighted boundedness results on L(1+log~(+α)L) of M_8 are investigated.