Аннотация
On a boundedness result of non-toroidal pseudo-differential operators Abstract.In this article, we prove boundedness results for θ-toroidal pseudo-differential operators generated by a differentiation operator with a non-periodic boundary condition.θ-toroidal pseudodifferential operators are a natural generalization of a toroidal one.As in the classical case, this class of operators act on a suitable test function space by weighting the Fourier transform "very well".Standard operations as adjoints, products and commutators with θ-toroidal pseudo-differential operators can be characterized by their θ-toroidal symbols.For pseudo-differential operators on R � , the symbol analysis is well developed.Here, we provide more complicated properties of the θ-toroidal pseudo calculus.Namely, we introduce a Holder space induced by a differentiation operator with a non-periodic boundary condition.Finally, for the elements of this space we prove theorems on boundedness of the operators acting on the specified functional spaces.Indeed, in this paper we continue a development of the so called "nonharmonic analysis" introduced in the recent papers of the authors.