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Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1
L.N. Gumilyov Eurasian National University.
L.N. Gumilyov Eurasian National University.
LuleƄ University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2011 (English)In: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 61, no 1, p. 7-26Article in journal (Refereed) Published
Abstract [en]

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

Place, publisher, year, edition, pages
2011. Vol. 61, no 1, p. 7-26
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-15588DOI: 10.1007/s10587-011-0014-1ISI: 000288512000002Scopus ID: 2-s2.0-79952771305Local ID: f1f5decf-8542-438d-9ec0-8df8139c5423OAI: oai:DiVA.org:ltu-15588DiVA, id: diva2:988562
Note
Validerad; 2011; 20110408 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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