Besov type function spaces defined on metric-measure spaces

The purpose of this article is to study the Besov type function spaces for maps which are defined on abstract metric-measure spaces. We extend some of the embedding theorems of the classical Besov spaces to the setting of abstract spaces.     

齐型空间上的分数次积分算子

An equivalent definition of fractional integral on spaces of homogeneous type is given.The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed.     

Essential norms of integral operators on spaces of analytic functions

This note aims at investigating the essential norms of integral operators on Banach spaces of analytic functions. We study the essential norm of _Ig$I_g$ on some classical Banach spaces (the Bloch space, BMOA$BMOA$ and the Dirichlet space). The essential norms of the Volterra type operator _Tg$T_g$ on the Bloch space are given by the distance from the logarithmic Bloch function to the little logarithmic Bloch space. The essential norms of the little Hankel operator are also investigated.     

Inner functions on spaces of homogeneous type

One shows that the methods of M. Hakim, N. Sibony, and E. Løw, used by them for the construction of inner functions in a sphere, can be applied also in a more general situation. The fundamental result of the paper is: For any positive continuous function H on the unit sphere S of the space ^d, there exists a real function u, harmonic in the unit ball, such that the function u is bounded in B and ¦u¦ =H almost everywhere on S.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 7–14, 1983.     

Singular integral operators on Triebel-Lizorkin spaces of para-accretive type

In this article, we study the boundedness of singular integral operators acting on Triebel-Lizorkin spaces of para-accretive type and show a Tb theorem on these spaces, which extends previous results in David, Journé and Semmes (1985) [3], Han (1994) [9], Han, Lee and Lin (2004) [10], Han and Sawyer (1990) [12], Lin and Wang (2009) [15], Wang (1999) [22].     

Conformally flat pseudo-symmetric spaces of constant type

We give the complete classification of conformally flat pseudo-symmetric spaces of constant type.     

Maximal commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of homogeneous type

Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, via a new Cotlar type inequality linking commutators and corresponding maximal operators, a weighted Lp(X) estimate with general weights and a weak type endpoint estimate with A₁(X) weights are established for maximal operators corresponding to commutators of BMO(X) functions and singular integral operators with non-smooth kernels.     

An integral representation of functions

We obtain an integral representation of functions of real variables which can be considered (at least formally) as some analog of the Fourier formula.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 47, pp. 67–72, 1974.     

Heat kernels on metric spaces and a characterisation of constant functions

Using the Dirichlet forms theory, we prove that when the locally compact measure metric space (X,,m) is the state space of a Markov process with transition density p(t,x,y) bounded from the above by where is a function satisfying certain integrability condition, then the following statement holds: when u L²(X) and then u is a constant function.This work is partially supported by a KBN grant no. 2-PO3A-028-22.Mathematics Subject Classification (2000): primary 60J35, secondary 46E35     

Area integral functions for sectorial operators on L spaces

Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^infin functional calculus of sectorial operators on L^p-spaces hold true when the square functions are replaced by the area integral functions.     

Theory of integral operators in spaces of measurable vector functions

Translated from Issledovaniya po Prikladnoi Matematike, No. 12, pp. 162–174, 1984.     

Volterra integral operators in spaces of functions of two variables

The solvability in the spaces C and L_p, 1p , of the linear equation

C-Z type singular integral operators on weighted Herz-type Hardy spaces

The HK _q ^a,p (w₁,w₂) and HK _q ^a,p (w₁, w₂) boundedness of C-Z type singular integral operators are proved.     

Boundedness for multilinear fractional integral operators on Herz type spaces

In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.     

C-Z type singular integral operators on weighted Herz-type Hardy spaces

The HK _q ^a,p (w₁,w₂) and HK _q ^a,p (w₁, w₂) boundedness of C-Z type singular integral operators are proved.