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

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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 -