Boundedness of the potential operators and their commutators in the local "complementary" generalized variable exponent Morrey spaces on unbounded sets
ANNALS OF FUNCTIONAL ANALYSIS, cilt.11, sa.2, ss.423-438, 2020 (SCI-Expanded, Scopus)
- 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.