TY - JOUR
T1 - Fractional operators of variable order from variable exponent Morrey spaces to variable exponent Campanato spaces on quasi-metric measure spaces with growth condition
AU - Rafeiro, Humberto
AU - Samko, Stefan
N1 - Publisher Copyright:
© Università degli Studi di Napoli "Federico II" 2021.
PY - 2024/4
Y1 - 2024/4
N2 - We study fractional potential of variable order on a bounded quasi-metric measure space (X,d,μ) as acting from variable exponent Morrey space Lp(·),λ(·)(X) to variable exponent Campanato space Lp(·),λ(·)(X). We assume that the measure satisfies the growth condition μB(x,r)⩽Crγ, the distance is θ-regular in the sense of Macías and Segovia, but do not assume that the space (X,d,μ) is homogeneous. We study the situation when γ-λ(x)⩽α(x)p(x)⩽γ-λ(x)+θp(x), and pay special attention to the cases of bounds of this interval. The left bound formally corresponds to the BMO target space. In the case of right bound a certain “correcting factor” of logarithmic type should be introduced in the target Campanato space.
AB - We study fractional potential of variable order on a bounded quasi-metric measure space (X,d,μ) as acting from variable exponent Morrey space Lp(·),λ(·)(X) to variable exponent Campanato space Lp(·),λ(·)(X). We assume that the measure satisfies the growth condition μB(x,r)⩽Crγ, the distance is θ-regular in the sense of Macías and Segovia, but do not assume that the space (X,d,μ) is homogeneous. We study the situation when γ-λ(x)⩽α(x)p(x)⩽γ-λ(x)+θp(x), and pay special attention to the cases of bounds of this interval. The left bound formally corresponds to the BMO target space. In the case of right bound a certain “correcting factor” of logarithmic type should be introduced in the target Campanato space.
KW - 26A33
KW - 46E30
KW - Campanato space
KW - Fractional operator
KW - Morrey space
KW - Quasi-metric measure space
UR - http://www.scopus.com/inward/record.url?scp=85113984861&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85113984861&partnerID=8YFLogxK
U2 - 10.1007/s11587-021-00639-4
DO - 10.1007/s11587-021-00639-4
M3 - Article
AN - SCOPUS:85113984861
SN - 0035-5038
VL - 73
SP - 803
EP - 818
JO - Ricerche di Matematica
JF - Ricerche di Matematica
IS - 2
ER -