Study On Properties Of Small Hankel Operator On Harmonic Bergman Space

In recent years,many scholars are very interested in the study of the properties of Toeplitz operators and Hankel operators in the Bergman space.The study of the compactness,boundedness,positivity,exchangeability,and multiplication of operators has always been the important issues which exploration of the theory of operators in the functional space,and promote the development of disciplines such as wavelet analysis,quantum mechanics,and dynamic systems.Ruben Martinez Avendano conducted a series of studies on small Hankel operators in Hardy space,and obtained a more complete description of the nature and structure of small Hankel operator algebras.Tomoko Osawa studied the large Hankel operator.As we all know,the nature of the operators in different spaces may be very different.Furthermore,some scholars have studied the small Hankel operator and the large Hankel operator on the Bergman space.In fact,some scholars have already said that many properties of the Toeplitz operator on the Bergman space also have similar properties to the small Hankel operator.In this paper,we study the properties of the small Hankel operator and the large Hankel operator with the sign of the radial function on the harmonic Bergman space on the unit disk.By constructing a series of symbols??_k?related to its sign function,some We get some conclusions about the properties of the large Hankel and small Hankel operators.This paper is divided into four chapters:The first chapter mainly introduces the development history and research status quo and background of function space and operator theory.Chapter 2 describes the concepts of Hardy space,Harmonic Bergman space and Toeplitz operator and Hankel operator.In Chapter 3,the boundedness,compactness and positive definiteness of Toeplitz operators on the harmonic Bergman space on unit disk are expounded.In Chapter 4,we mainly discuss some of the equivalences between some of the properties of the large Hankel operator and the small Hankel operator with the radial function as a symbol and the series of numbers??_k?we construct with its symbol.