Mathematics & Physics 2017, 10(1), 83–95 УДК 517.98 Embedding Theorems for Functional Spaces Associated with a Class of Hermitian Forms Anastasiya S.Peicheva∗ Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 28.05.2016, received in revised form 10.06.2016, accepted 14.11.2016 We prove embedding theorems into the scale of Sobolev-Slobodetskii spaces for functional spaces associated with a class of Hermitian forms. <...> More precisely we consider the Hermitian forms constructed with the use of the first order differential matrix operators with injective principal symbol. <...> The results are valid for both coercive and non-coercive forms. <...> It is well known that integro-differential Hermitian forms are closely related to the generalized setting of mixed boundary value problems for strongly elliptic equations and systems, as well as the existence and uniqueness theorems for such problems (see, for example, [1–6], and other). <...> We prove embedding theorems into the scale of Sobolev-Slobodetskii spaces for functional spaces associated with one class of Hermitian forms. <...> More precisely, we consider the Hermitian forms constructed with the use of the first order matrix differential operators with the injective principal symbol. <...> The results are valid for both coercive and non-coercive forms. 1. <...> Function spaces Let D be a bounded domain with Lipschitz boundary in Euclidean space Rn, n 2, with ∂|α| coordinates x = (x1, . . . ,xn). <...> For some multi-index α = (α1, . . . ,αn) we will write ∂α for the partial derivative ∂xα1 are disappearing in some (one-sided) neighborhood S in D. We will write Lq(D), 1 q +∞, for standard normed Lebesgue spaces of functions over D. We also write Hs(D), s ⊂ N, for the Sobolev space of functions whose weak derivatives up to the order s belong to L2(D). <...> Similarly, Hs(∂D), s ⊂ N, stand for the Sobolev space on the boundary of domain ∂D of functions whose weak derivatives up to the order s belong to L2(∂D). <...> Let the spaceHs 0(D) stand for the closure of space C∞ ⃝ Siberian Federal University. <...> For positive non-integer s we denote by Hs(D) the Sobolev-Slobodetskii space <...>