Quantitative norm convergence of double ergodic averages associated with two commuting group actions (CROSBI ID 207463)
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Kovač, Vjekoslav
engleski
Quantitative norm convergence of double ergodic averages associated with two commuting group actions
We study double averages along orbits for measure preserving actions of A^w, the direct sum of countably many copies of a finite abelian group A. In this article we show an L^p norm-variation estimate for these averages, which in particular reproves their convergence in L^p for any finite p and for any choice of two L^\infty functions. The result is motivated by recent questions on quantifying convergence of multiple ergodic averages.
mean ergodic theorem ; multiple ergodic averages ; norm convergence ; Cantor group ; multilinear operator
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