Título inglés | Multiparameter pointwise ergodic theorems for Markov operators on L∞. |
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Título español | Teoremas ergódicos puntuales multiparamétricos para operadores de Markov sobre L∞. |
Autor/es | Sato, Ryotaro |
Organización | Dep. Math. Sch. Sci. Okayama Univ., Okayama, Japón |
Revista | 0214-1493 |
Publicación | 1994, 38 (2): 395-410, 9 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p < ∞ the averages Anf = (n + 1)-d Σ0≤ni≤n P1n1 P2n2 ... Pdnd f (n ≥ 0) converge almost everywhere if and only if there exists an invariant and equivalent finite measure λ for which the Radon-Nikodym derivative v = dλ/dμ is in the dual space Lp'(X,F,μ). Next we study the case in which exists p1, with 1 ≤ p1 ≤ ∞, such that for every f in Lp(X,F,μ) the limit function belongs to Lp1(X,F,μ). We give necessary and sufficient conditions for this problem. |
Clasificación UNESCO | 120217 |
Palabras clave español | Teoría ergódica ; Espacio de medida ; Teorema de Radon-Nikodym |
Código MathReviews | MR1316635 |
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