ABSTRACT In this work, we extend the result of G. David and J.—L. Journe about the 2 boundedness of Calderon—Zygmund operators on the space L , to other spaces of functions or distributions. We also study, along the same lines, fractional integral operators, pseudodifferential operators, and other operators defined by singular kernels. The main tools used are some discrete decomposition techniques for spaces of distributions. In particular, we consider the atomic and molecular decompositions of the Triebel—Lizorkin spaces obtained by M. Frazier and B. Jawerth in their work about the ip —transform. By the properties of the Triebel—Lizorkin spaces, the results that we obtain immediately translate to more classical spaces such as Lebesgue, Hardy, Lipschitz, Besov, Bessel Potential, and Sobolev spaces. 1980 Mathematics Subject Classification (1985 Revision) . Primary 43B20 Secondary 46F12, 47G05. Key words and phrases . Singular integrals. Calderon—Zygmund operators. Pseudo- differential operators. Atomic decompositions. Distribution spaces. Triebel—Lizorkin spaces. v
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