On a Kudryavtsev type function space

In the paper we introduce a Kudryavtsev type space, the norm of which contains a differential operator called the multiweighted derivative. This type of spaces has been studied in details for power weights. Here we consider general weights. The main result of the paper is the proof of the existence of a generalized polynomial, to which functions of this space stabilize at a singular point, so that the coefficients of this polynomial can be considered as the characteristics of the behaviour of a function nearby this singularity.