منابع مشابه
On weighted critical imbeddings of Sobolev spaces
Our concern in this paper lies with two aspects of weighted exponential spaces connected with their role of target spaces for critical imbeddings of Sobolev spaces. We characterize weights which do not change an exponential space up to equivalence of norms. Specifically, we first prove that Lexp tα(χB) = Lexp tα(ρ) if and only if ρq ∈ Lq with some q > 1. Second, we consider the Sobolev space W ...
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We consider the imbedding inequality ‖ ‖ Lr(R d ) ≤ Sr,n,d ‖ ‖Hn(Rd); H n(R) is the Sobolev space (or Bessel potential space) of L2 type and (integer or fractional) order n. We write down upper bounds for the constants Sr,n,d, using an argument previously applied in the literature in particular cases. We prove that the upper bounds computed in this way are in fact the sharp constants if (r = 2 ...
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ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 2011
ISSN: 1139-1138,1988-2807
DOI: 10.1007/s13163-011-0087-2