Equations in Convolutions in a Bounded Region

Abstract

CONTENTSIntroduction § 1. Function spaces § 2. Factorization of a homogeneous function § 3. Convolution operator with constant symbols in R^n and R^n_+ § 4. Smooth convolution operators in R^n_+ § 5. Statement of the general boundary problem with \kappa \ge 0 for a smooth operator in R^n_+ § 6. Apriori estimate and right regularizer for an operator with a constant symbol § 7. Operators with variable symbols in R^n and in R^n_+, 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 \kappa < 0 for smooth operators in R^n_+ § 12. Apriori estimate and construction of the right regularizer § 13. Equations with potentials having a symbol depending on x § 14. Equations with rational symbolsAppendix 1. Lemmas on commutationAppendix 2. Formula for change of variablesReferences