ИСТИНА

We present a survey of results related to properties and interrelation of some Perron type integrals defined by various symmetric derivates and solving the problem of recovering the coefficients of convergent trigonometric series by generalized Fourier formulas. A special emphasis is given to classes of integrable functions with continuous primitives. In particular we show that the Marcinkiewicz–Zygmund integral defined by symmetric Borel derivative remains to be essentially more general than Burkill’s SCP-integral and James’ P2-integral on such a class of integrable functions.