. . . . "RIV/67985840:_____/10:00339255" . . . "264604" . . "P(GA201/05/2033), P(GA201/08/0383), Z(AV0Z10190503)" . . "DE - Spolkov\u00E1 republika N\u011Bmecko" . . "Koskela, P." . . . "3"^^ . "Shanmugalingam, N." . "Interpolation properties of Besov spaces defined on metric spaces"@en . "000275649300005" . "Interpolation properties of Besov spaces defined on metric spaces" . . "1"^^ . "Mathematische Nachrichten" . . "17"^^ . . "2" . "Gogatishvili, Amiran" . . . "Let X = (X, d, \u03BC) be a doubling metric measure space. We define so called Besov spaces B_{p,q}^\u03B1(X). We will show that if a doubling metric measure space (X, d, \u03BC) supports a (1, p)-Poincar\u00E9 inequality, then the Besov space B_{p,q}^\u03B1(X) coincides with the real interpolation space (L_{p}(X), KS_{1,p}(X))_{ \u03B1 ,q}, where KS_{1,p}(X) is the Sobolev space defined by Korevaar and Schoen . This result is used to prove the imbedding theorems."@en . . "[3C292D8CA743]" . . "Besov spaces; Sobolev spaces; real interpolation method; K-functional; metric measure space; doubling measure space; embedding theorems"@en . . "Interpolation properties of Besov spaces defined on metric spaces"@en . "RIV/67985840:_____/10:00339255!RIV10-AV0-67985840" . "Interpolation properties of Besov spaces defined on metric spaces" . "Let X = (X, d, \u03BC) be a doubling metric measure space. We define so called Besov spaces B_{p,q}^\u03B1(X). We will show that if a doubling metric measure space (X, d, \u03BC) supports a (1, p)-Poincar\u00E9 inequality, then the Besov space B_{p,q}^\u03B1(X) coincides with the real interpolation space (L_{p}(X), KS_{1,p}(X))_{ \u03B1 ,q}, where KS_{1,p}(X) is the Sobolev space defined by Korevaar and Schoen . This result is used to prove the imbedding theorems." . . . "283" . . "0025-584X" .