Boundedness of the potential operators and their commutators in the local "complementary" generalized variable exponent Morrey spaces on unbounded sets

AYKOL KOCAKUŞAKLI C., Badalov X. A., Hasanov J. J.

ANNALS OF FUNCTIONAL ANALYSIS, cilt.11, sa.2, ss.423-438, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s43034-019-00012-5
  • Dergi Adı: ANNALS OF FUNCTIONAL ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.423-438
  • Anahtar Kelimeler: Riesz potential, Fractional maximal operator, Maximal operator, Local "complementary" generalized variable exponent Morrey space, Hardy-Littlewood-Sobolev-Morrey type estimate, BMO space, MAXIMAL-FUNCTION, SINGULAR-OPERATORS, LEBESGUE SPACES
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we prove a Sobolev-Spanne type M p(center dot),. {x0} (O). Mq(center dot),. {x0} (O)theorem for the potential operators I a, where M p(center dot),. {x0} (O) is local "complementary" generalized Morrey spaces with variable exponent p( x),.(r) is a general function defining the Morrey-type norm and O is an open unbounded subset of Rn. In addition, we prove the boundedness of the commutator of potential operators [b, I a] in these spaces. In all cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on.(x, r), which do not assume any assumption on monotonicity of.(x, r) in r.