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In this paper we construct two large classes of BMOA functions with BMOA norm equal to the H2 norm, respecting equal to the H norm. We also determine all functions in the disc algebra with BMOA norm equal to the Bloch norm.  相似文献   

3.
Shamoyan  R. F. 《Mathematical Notes》2003,73(5-6):711-723
In this paper, we describe coefficient multipliers, study the action of fractional derivatives of spaces of BMOA type and the action of Toeplitz operators in these classes.  相似文献   

4.
We prove that the Bourgain algebra of the polydisk algebra A(Δn) is A(Δn) itself and disprove the tightness of some algebras of analytic functions; in particular that of H(BE).  相似文献   

5.
The exact approximation orders for the classes H q Ω are calculated for the case in which Ω(t) contains both power and logarithmic multipliers. For these classes, the exact orders of best approximation by analogs of “improper” hyperbolic crosses are also obtained.  相似文献   

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In this article,we characterize the boundedness and compactness of extended Cesàro operators on the spaces BMOA by the Carleson measures in the unit ball.Mean-while,we study the pointwise multipliers o...  相似文献   

8.
We obtain order-sharp estimates of the orthogonal projection widths of the classes B p,θ Ω of periodic functions of several variables whose majorant of the mixed moduli of continuity contains both exponential and logarithmic multipliers.  相似文献   

9.
Avetisyan  K. L. 《Mathematical Notes》2004,75(3-4):453-461
For n-harmonic functions on the unit polydisk in the space $\mathbb{C}^n $ we define g-functions of Littlewood--Paley type and establish L p-inequalities related to them. In the present paper, the main theorems deal with the extension of results of Littlewood, Paley, and Flett to the polydisk and their generalizion to fractional derivatives of arbitrary order. This gives an answer to a question posed by Littlewood.  相似文献   

10.
Let L be a non-negative self-adjoint operator acting on L2(X) where X is a space of homogeneous type. Assume that L generates a holomorphic semigroup etL whose kernels pt(x,y) have Gaussian upper bounds but there is no assumption on the regularity in variables x and y. In this article, we study weighted Lp-norm inequalities for spectral multipliers of L. We show that sharp weighted Hörmander-type spectral multiplier theorems follow from Gaussian heat kernel bounds and appropriate L2 estimates of the kernels of the spectral multipliers. These results are applicable to spectral multipliers for large classes of operators including Laplace operators acting on Lie groups of polynomial growth or irregular non-doubling domains of Euclidean spaces, elliptic operators on compact manifolds and Schrödinger operators with non-negative potentials.  相似文献   

11.
Boundedness (resp. compactness) of weighted composition operators Wh,φ acting on the classical Hardy space H2 as Wh,φf=h(fφ) are characterized in terms of a Nevanlinna counting function associated to the symbols h and φ whenever h∈BMOA (resp. h∈VMOA). Analogous results are given for Hp spaces and the scale of weighted Bergman spaces. In the latter case, BMOA is replaced by the Bloch space (resp. VMOA by the little Bloch space).  相似文献   

12.
In this note, we show that a quasi-free Hilbert module R defined over the polydisk algebra with kernel function k(z,w) admits a unique minimal dilation (actually an isometric co-extension) to the Hardy module over the polydisk if and only if S ?1(z, w)k(z, w) is a positive kernel function, where S(z,w) is the Szegö kernel for the polydisk. Moreover, we establish the equivalence of such a factorization of the kernel function and a positivity condition, defined using the hereditary functional calculus, which was introduced earlier by Athavale [8] and Ambrozie, Englis and Müller [2]. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. The proof works for a wider class of Hilbert modules in which the Hardy module is replaced by more general quasi-free Hilbert modules such as the classical spaces on the polydisk or the unit ball in ? m . Some consequences of this more general result are then explored in the case of several natural function algebras.  相似文献   

13.
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R~d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R~d).  相似文献   

14.
The connection between Belinsky?CDveyrin?CMalamud??s theorem on multipliers and some other known theorems on multipliers in the spaces L 1 and C is clarified. It is shown that Belinsky?CDveyrin?CMalamud??s theorem can be obtained from them. The relevant examples of multipliers in the spaces L 1 and C indicating the nonequivalence of the compared theorems are presented.  相似文献   

15.
Following the lines of [13] we introduce the classes of mixed smoothness Lαp(Rn), Lαp(Zn) for a multi-index α = (α1,…, αn). Such classes are naturally tied up with the study of semi-elliptic differential and difference equations.Besides a brief presentation of such classes, we concentrate our research on the study of mixed homogeneous multipliers with homogeneity β = (β1, …, βn) and their preservation of mixed homogeneous Hölder classes Lα, for a different multi-index α.In the last paragraph we apply the results to produce various improvements of the classical Schauder's estimates, for differential and difference equations, in the parabolic and elliptic case.  相似文献   

16.
In this paper, we consider a class of Fourier multipliers whose symbols are controlled by a polynomial on starlike Lipschitz surfaces and get the L2 boundedness of these operators on Sobolev spaces and their endpoint estimates.  相似文献   

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We obtain a decomposition for multivariable Schur-class functions on the unit polydisk which, to a certain extent, is analogous to Agler's decomposition for functions from the Schur-Agler class. As a consequence, we show that d-tuples of commuting strict contractions obeying an additional positivity constraint satisfy the d-variable von Neumann inequality for an arbitrary operator-valued bounded analytic function on the polydisk. Also, this decomposition yields a necessary condition for solvability of the finite data Nevanlinna-Pick interpolation problem in the Schur class on the unit polydisk.  相似文献   

19.
We show that the Weyl correspondence and the concept of a Moyal multiplier can be naturally extended to generalized function classes that are larger than the class of tempered distributions. This generalization is motivated by possible applications to noncommutative quantum field theory. We prove that under reasonable restrictions on the test function space E ? L2, any operator in L2 with a domain E and continuous in the topologies of E and L2 has a Weyl symbol, which is defined as a generalized function on the Wigner-Moyal transform of the projective tensor square of E. We also give an exact characterization of the Weyl transforms of the Moyal multipliers for the Gel??fand-Shilov spaces S ?? ?? .  相似文献   

20.
We study the weighted composition operators Wh,on Hardy space H2(B) whenever h ∈ BMOA(resp.h ∈ VMOA).Analogous results are given for Hp(B) spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space(resp.VMOA by the little Bloch space).  相似文献   

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