Boundedness of some sublinear operators and their commutators on generalized local Morrey spaces

Balakishiyev A. S., Gadjieva E. A., Gurbuz F., ŞERBETÇİ A.

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, cilt.63, sa.11, ss.1620-1641, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63 Sayı: 11
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1080/17476933.2017.1403423
  • Dergi Adı: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1620-1641
  • Anahtar Kelimeler: Sublinear operator, fractional integral operator, generalized local Morrey spaces, SINGULAR INTEGRAL-OPERATORS, DIRICHLET PROBLEM, MAXIMAL OPERATOR, SUFFICIENT CONDITIONS, ELLIPTIC-EQUATIONS
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paperwe prove the boundedness of certain sublinear operators T , a, a. 0, n , generated by fractional integral operators with rough kernels . Ls( Sn- 1), s > 1, from one generalized local Morrey space LM {x0} p,.1 to another LM {x0} q,.2, 1 < p < q < 8, 1p - 1q = a n, and from the space LM {x0} 1,.1 to the weak space WLM {x0} q,.2, 1 < q < 8, 1 - 1q = a n. In the case b belongs to the local Campanato space LC {x0} p2,. and T , b, a is a linear operator, we find the sufficient conditions on the pair (.1,.2) which ensures the boundedness of the commutator operators T , b, a from LM {x0} p1,.1 to LM {x0} q,.2, 1 < p < 8, 1p = 1 p1 + 1 p2, 1q = 1p - a n, 1 q1 = 1 p1 - a n. In all cases the conditions for the boundedness of T , a are given in terms of Zygmund- type integral inequalities on (.1,.2), which do not assume any assumption on monotonicity of.1,.2 in r.