EQUATIONS IN CONVOLUTIONS IN A BOUNDED REGION

Abstract

CONTENTS Introduction § 1. Function spaces § 2. Factorization of a homogeneous function § 3. Convolution operator with constant symbols in and § 4. Smooth convolution operators in § 5. Statement of the general boundary problem with for a smooth operator in § 6. Apriori estimate and right regularizer for an operator with a constant symbol § 7. Operators with variable symbols in and in , and their boundedness § 8. Right regularizer in a half-space and in the whole space in the case of an operator with variable symbol § 9. Operators in a bounded region. Formulation of the main theorem § 10. Apriori estimate and right regularizer in a bounded region § 11. General equation with potentials with for smooth operators in § 12. Apriori estimate and construction of the right regularizer § 13. Equations with potentials having a symbol depending on § 14. Equations with rational symbols Appendix 1. Lemmas on commutation Appendix 2. Formula for change of variables References