Samra Sadikovic

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In this paper we prove that on the 3-series field H1 cannot be defined by means of the V-conjugation. In other words, the norms kfkH1 and k ˜ fkL1 are not equivalent in the case of the 3-series field. This gives a new proof to the result of Memić [7], which answers a question raised by P. Simon [13]. Also, we prove that the mean value of function f ∈ L1(G) on the coset IN−1(x) is dominated by either MN−1 or MN on some translated element.


Maximal function; V-conjugation; Vilenkin groups


V-conjugation, maximal function, Vilenkin groups

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