Some properties of Sobolev algebras modelled on Lorentz spaces

Eryılmaz İ., Sağır Duyar B.

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, cilt.59, sa.1, ss.83-91, 2014 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 1
  • Basım Tarihi: 2014
  • Dergi Adı: STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.83-91
  • Anahtar Kelimeler: Sobolev spaces, Lorentz spaces, weak derivative, FP-algebras, weak factorization, multipliers, MULTIPLIERS
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this paper, firstly Lorentz-Sobolev spaces W-L(p,W-q) (k) (R-n) of integer order are introduced and some of their important properties are emphasized. Also, the Banach spaces A(L(pq))(k)(R-n) = L-1-(R-n)boolean AND W-L(p,q)(k) (R-n) (Lorentz-Sobolev algebras in the sense of H.Reiter) are studied. Then, using a result due to H.C.Wang, it is showed that Banach convolution algebras AkL(pq) (Rn) do not have weak factorization. Lastly, it is found that the multiplier algebra of A(L(pq))(k)(R-n) coincides with the measure algebra M (R-n) for 1 < p < infinity and 1 <= q < infinity.