TY - JOUR
T1 - BMO–VMO results for fractional integrals in variable exponent Morrey spaces
AU - Rafeiro, Humberto
AU - Samko, Stefan
N1 - Funding Information:
The research of H. Rafeiro was supported by a Research Start-up Grant of United Arab Emirates University, Al Ain, United Arab Emirates via Grant No. G00002994 . The research of S. Samko was supported by Russian Foundation for Basic Research under the grants 19-01-00223 .
Funding Information:
The research of H. Rafeiro was supported by a Research Start-up Grant of United Arab Emirates University, Al Ain, United Arab Emirates via Grant No. G00002994. The research of S. Samko was supported by Russian Foundation for Basic Research under the grants 19-01-00223.
Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/7
Y1 - 2019/7
N2 - We prove the boundedness of the fractional integration operator of variable order α(x) in the limiting Sobolev case α(x)p(x)=n−λ(x) from variable exponent Morrey spaces L p⋅,λ⋅ Ω into BMO (Ω), where Ω is a bounded open set. In the case α(x)≡ const, we also show the boundedness from variable exponent vanishing Morrey spaces VL p⋅,λ⋅ Ω into VMO (Ω). The results seem to be new even when p and λ are constant.
AB - We prove the boundedness of the fractional integration operator of variable order α(x) in the limiting Sobolev case α(x)p(x)=n−λ(x) from variable exponent Morrey spaces L p⋅,λ⋅ Ω into BMO (Ω), where Ω is a bounded open set. In the case α(x)≡ const, we also show the boundedness from variable exponent vanishing Morrey spaces VL p⋅,λ⋅ Ω into VMO (Ω). The results seem to be new even when p and λ are constant.
KW - BMO
KW - Fractional integral
KW - Riesz potential
KW - Variable exponent Morrey spaces
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U2 - 10.1016/j.na.2019.01.020
DO - 10.1016/j.na.2019.01.020
M3 - Article
AN - SCOPUS:85061671200
SN - 0362-546X
VL - 184
SP - 35
EP - 43
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -