Abstract: Some recent results related to the P-adic derivatives and integrals are surveyed. Applications of the Henstock-Kurzweil P-integral and the Perron P-integral to the problem of recovering the coefficients of series with respect to the Vilenkin system and the Haar system (both in one dimension and in higher dimensions) are discussed. The case of the continual analogue of the Vilenkin system is also considered.
Keywords: Henstock-Kurzweil integral, Perron integral, $\mathcal P$-adic derivate basis, variational measure, Walsh system, Vilenkin system, Haar system.
Classification (MSC2000): 26A39
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