On Imbedding Theorems for Besov Spaces of Functions Defined in General Regions

This paper is a continuation of the author's work Q7] concerning Besov spaces of functions defined in general regions; here we treat imbedding theorems. Our method is the same as that of the author's previous papers 5] and £7]. That is, we employ an integral representation which gives us Sobolev type inequalities with the aid of the theory of mean interpolation spaces due to Lions-Peetre Q3]. To prove the basic inequalities we shall make use of the idea due to O'Neil CIO] and Peetre pLl]. We denote by Q an open set in n -space R. Let l<p,? ^°°, and let 5 be a positive integer such that s<ⁿ. For measurable functions defined in @ we introduce the norm