Weak Triebel-Lizorkin Spaces

The dissertation is devoted to the characterizations of weak Triebel-Lizorkin spaces with consistent exponents and weak Triebel-Lizorkin spaces with variable exponents.The plan is the following:In Chapter 1,there are the literature review,notations and the statement of main results.In Chapter 2,equivalent quasi-norms of weak Triebel-Lizorkin spaces with consistent exponents in terms of Peetre’s maximal functions and an atomic decomposition of weak Triebel-Lizorkin spaces are proved.In Chapter 3,characterizations of weak Triebel-Lizorkin spaces with variable exponents by means of Peetre’s maximal functions,φ transform,atoms and molecules are proved.