On some spaces and integral operators in fourier- bessel harmonic analysis

This thesis has two aims. The first aim of this thesis is to investigate some function spaces in Fourier- Bessel harmonic analysis then to define B- Campanato space and to study some properties of this space. The second aim is to obtain boundedness of the singular integral operators (B- singular integral operators) on Fourier- Bessel harmonic analysis. For this purpose, firstly, definitions of B- singular integral operators and vector- valued B- singular integral operators are given and boundedness of these singular integral operators are obtained. Finally, definition of B- square function is given and boundedness of B- square function is proved by using boundedness of vector- valued B- singular integral operators.