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In the present paper we show that Lp -integrability near zero of a function on Vilenkin group G with nonnegative Fourier-Vilenkin coefficients implies Lp -integrability on G , if p is even integer. This is an analog of N. Wiener-S. Wainger result. A refinement of HausdorffYoung-F. Riesz inequality is obtained and several examples concerning embeddings of solid function spaces on G are given. Mathematics subject classification (2010): 43A75,43A15.

Wiener type theorems for Fourier-Vilenikin series with nonnegative coefficients and solid spaces