Triebel-lizorkin-lorentz spaces and integral operators on harmonic anaylysis

The limitations of the classical operators of harmonic analysis in various function spaces have been studied extensively by many mathematicians.L(p,q) Lorentz spaces, which were defined by George G. Lorentz in 1951, are one of the important subjects of harmonic analysis. Lorentz spaces constitute an important field in solving some internal problems in harmonic analysis, in physics and in solving mathematical partial derivatives in recent years.In addition, examining the limitations of integral operators in Lorentz spaces has an important place in some application areas. In this thesis, it is aimed to examine the properties of Triebel-Lizorkin-Lorentz spaces in harmonic analysis, which has been important in many mathematical fields in recent years, and the limitations of some integral operators in these spaces.