Properties Of Harmonic Besov Spaces

The main aim of this thesis is to establish some characterizations for har-monic Besov spaces.This thesis consists of four chapters and its arrangement is as follows.In the first chapter,we introduce the background of the studied problems and present the main results.In the second chapter,at first,we establish a characterization for harmonic Besov spaces by using the double integral which is defined on the unit disk.The result is stated as Theorem 2.3.1.Then we characterize harmonic Besov spaces in terms of Bergman metric,i.e.,Theorem 2.3.2.At last,we generalize Theorem 2.3.1 to the setting of higher dimensional spaces,which is formulate.d in Theorem 2.4.1.In the third chapter,by exploiting the n-th derivative of mappings,we give an equivalent condition for mappings which belong to harmonic Besov spaces,i.e.,Theorem 3.2.1.Furthermore,we generalize this result to the case of higher dimensional spaces,see Theorem 3.2.2.In the forth chapter,we give a necessary condition for mappings to belong to biharmonic Besov spaces.This result is formulated as Theorem 4.1.1.