Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University20805Research ArticleThe Laplace’ quasi-operator in quasi-Sobolev spacesAl-DelfiJawad KPostgraduate Student, Dept. of Equations of Mathematical Phisicsrassian71@mail.ruSouth Ural State University (National Research University)15062013172131618022020Copyright © 2013, Samara State Technical University2013The quasi-Sobolev spaces notion introduced in the article is based on the quasinorms concept. Completeness of these spaces on the appropriate quasi-norms is proved and the continuous embedding of these spaces is shown in the work. Also Laplace’ and Green’s quasi-operators concepts are introduced; it is shown that these quasi-operators are toplinear isomorphisms.quasi-normquasi-Banach spacequasi-Sobolev spacesLaplace’ quasioperatorGreen’s quasi-operatorквазинормаквазибанахово пространствоквазисоболевы пространстваквазиоператор Лапласаквазиоператор Грина[Трибель Х. Теория интерполяций. Функциональные пространства. Дифференциальные операторы. М.: Мир, 1980. 664 с.][Ладыженская О. А., Уральцева Н. Н., Линейные и квазилинейные уравнения эллиптического типа. М.: Наука, 1973. 578 с.][Al-Saphory R., Al-Janabi A., Al-Delfi J. Quasi-Banach Space for the Sequence Space lp, where 0 < p № 1 / Journal of Education College, 3. Baghdad, Iraq: University of AlMustansriyah, 2007. Pp. 285–295.]