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- Abdikalikova, Zamira, et al.
(författare)
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Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1
- 2011
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Ingår i: Czechoslovak Mathematical Journal. - : Institute of Mathematics, Czech Academy of Sciences. - 0011-4642 .- 1572-9141. ; 61:1, s. 7-26
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Tidskriftsartikel (refereegranskat)abstract
- We consider a new Sobolev type function space called the space with multiweighted derivatives W-p(n),(alpha) over bar, where (alpha) over bar = (alpha(0), alpha(1), ......, alpha(n)), alpha(i) is an element of R, i = 0, 1,......,n, and parallel to f parallel to W-p(n),((alpha) over bar) = parallel to D((alpha) over bar)(n)f parallel to(p) + Sigma(n-1) (i=0) vertical bar D((alpha) over bar)(i)f(1)vertical bar, D((alpha) over bar)(0)f(t) = t(alpha 0) f(t), d((alpha) over bar)(i)f(t) = t(alpha i) d/dt D-(alpha) over bar(i-1) f(t), i = 1, 2, ....., n. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W-p,(alpha) over bar(n) -> W-q,(beta) over bar,(m) when 1 <= q < p < infinity, 0 <= m < n
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