Integral Representations of Functions and Imbedding Theorems, Volume 1

analogous apply approach arbitrary assertion assume averaging basis belonging bounded coincides compact completes components condition Consequently Consider constant contained continuous coordinate corresponding cube defined definition denote depending derivative differentiable easily equal equation equivalent estimate example exists extend finite follows formula function f given holds identity independent inequality integral integral representations Lemma Let us define Lloc G Lp G Math mean measurable natural norm obtain Obviously open set operator P₁ parallelepiped parameters particular polynomial positive present proof properties prove region G replace represented respect result right-hand member satisfied sense Sobolev space subsection sufficiently supp Suppose Theorem Theorem 3.5 trace transformation Transl valid values variable vector virtue write zero