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Download fileSingular integrals with rough kernals and BMO spaces associated to operators
thesis
posted on 28.03.2022, 21:21 by Georges NaderThe purpose of this thesis is to study the new criterion for boundedness of some singular integrals. The main results of this thesis are presented in four parts. --1. Recall the Hörmander condition for boundedness of singular integrals which has been an important result of the Calderón-Zygmund theory. -- 2. Discuss a new criterion for singular integral operators to be bounded on Lp(X), 1< p < ∞ , where X is a space of homogeneous type. This criterion is an improvement of the Hörmander condition and it has had many applications in recent research of singular integrals in the last 20 years. -- 3. Discuss new function spaces which suit these operators such as BMOA spaces associated to operators. -- 4. Use these results to study the functional calculus of operators satisfying certain kernel estimates.