L^p Boundedness for Parabolic Littlewood-Paley Operators with Rough Kernels Belonging to Block Spaces

This paper is primarily concerned with the proof of the Lp boundedness of parabolic Littlewood-Paley operators with kernels belonging to certain block spaces. Some known results are essentially extended and improved.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

Let O（PτL be the oscillation of the Possion semigroup associated with the parabolic Hermite operator = t-△＋｜x｜2. We show that O（PτL） is bounded from LP （Rn＋1） into itself for 1 〈 p 〈 ∞, bounded from L1（Rn＋l） into weak-L1（Rn＋1） and bounded from Lc∞（Rn＋1） into BMO（Rn＋1）. In the case p = ∞ we show that the range of the image of the operator O（PτL） is strictly smaller than the range of a general singular operator.

THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS

The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.

Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.

The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (L^q , L^p )~α (R^n) Spaces

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.

LITTLEWOOD-PALEY THEOREM FOR SCHR DINGER OPERATORS

Let H be a Schroedinger operator on R^n. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.

LITTLEWOOD-PALEY OPERATORS AND MARCINKIEWICZ INTEGRAL ON GENERALIZED CAMPANATO SPACES

Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.

Parameterized Littlewood-Paley Operators on Weighted Herz Spaces

The strong type and weak type estimates of parameterized Littlewood-Paley operators on the weighted Herz spaces Kq α,p（ω1,ω2） are considered. The boundednessof the commutators generated by BMO functions and parameterized Littlewood-Paley operators are also obtained.

Boundedness of the Littlewood-Paley Operator,the Function g(f),on BMO(T)

Littlewood-Paley operator,the function g(f), is considered as an operator on BMO(T). It is proved that if f E BMO (T), then g(f)∈BMO (T) and there is a constant C that is independent of f such that ‖g(f)‖_* ≤C‖f‖_*. Moreover,we have got the further results.

Time-Optimal Control Problem for <i>n</i>×<i>n</i>Co-Operative Parabolic Systems with Control in Initial Conditions

In this paper, time-optimal control problem for a liner n× n co-operative parabolic system involving Laplace operator is considered. This problem is, steering an initial state y(0)=u?, with control u?so that an observation y(t) hitting a given target set in minimum time. First, the existence and uniqueness of solutions of such system under conditions on the coefficients are proved. Afterwards necessary and sufficient conditions of optimality are obtained. Finally a scaler case is given.

THE CONVERGENCE OF A DOMAIN DECOMPOSITION ALGORITHM FOR PARABOLIC PROBLEMS

At recent, Hourgat et gave a domain decomposition algorithm for elliptic problems which can be implemented in parallel. Many numerical experiments have illustrated its efficiency. In the present paper, we apply this algorithm to solve the discrete parabolic problems, analyse its convergence and show that its convergence rale is about (1 - 2p + σp2 ) which is nearly optimal and independent of the parameter τ, where σ τ O((1 +H )(1 + ln(H / h))2 ). 0 【 p 【 1 / σ,τ,h,H are the time step size, finite element parameter and subdomain diameter, respectively.

Extinction of Weak Solutions for Nonlinear Parabolic Equations with Nonstandard Growth Conditions

This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.

Characterizations of product Hardy space associated to Schrodinger operators

Let L1 and L2 be the Schrodinger operators on Rn and Rm, respectively. By using different maximal functions and Littlewood-Paley g function on distinct variables, in this paper,some characterizations for functions in the product Hardy space HL1,L21(R^n×R^m) associated to operators L1 and L2 are obtained.

Multilinear Commutators of Sublinear Operators on Triebel-Lizorkin Spaces

In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.

Associated Hermite Polynomials Related to Parabolic Cylinder Functions

In analogy to the role of Lommel polynomials ?in relation to Bessel functions Jv(z) the theory of Associated Hermite polynomials in the scaled form ?with parmeter v to Parabolic Cylinder functions Dv(z) is developed. The group-theoretical background with the 3-parameter group of motions M(2) in the plane for Bessel functions and of the Heisenberg-Weyl group W(2) for Parabolic Cylinder functions is discussed and compared with formulae, in particular, for the lowering and raising operators and the eigenvalue equations. Recurrence relations for the Associated Hermite polynomials and for their derivative and the differential equation for them are derived in detail. Explicit expressions for the Associated Hermite polynomials with involved Jacobi polynomials at argument zero are given and by means of them the Parabolic Cylinder functions are represented by two such basic functions.

复Banach空间上推广的Roper-Suffridge延拓算子

本文研究了推广的Roper-Suffridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Suffridge算子在复Banach空间单位球上保持ρ次抛物形β型螺形映照及强α次殆星形映照的性质,由此得到复Hilbert空间上推广的Roper-Suffridge算子的相应性质,推广了已有的结论.

核函数属于F_α(S^(n-1))空间中的抛物Littlewood-Paley算子的L^p有界性

该文证明了在一类较弱的条件下具有粗糙核的抛物Littlewood-Paley算子在L^p空间中的有界性,本质推广了一些已知结果.

抛物星形映射的一个子族与Roper-Suffridge算子

首先,从几何的视角引入了一类抛物星形映射子族.其次,给出欧氏空间单位球上该映射族与α次强β型螺形映射族之间的关系,同时证明了Roper-Suffridge算子在单位球上保持该类映射族的性质.作为推论,可以得到一些熟知的结果.

抛物型粗糙核Littlewood-Paley算子在齐次Triebel-Lizorkin空间上的有界性

当核函数属于块空间B0q,-1/2(Sn-1)时,得到了抛物型Littlewood-Paley算子在齐次Triebel-Lizorkin空间F.sp,q(Rn)上的有界性。