Abstract

The analysis of function spaces is particularly relevant in several areas of Mathematics such as differential and integral equations. Among function spaces, the weighted function spaces turn out to be suitable for the analysis of boundary value problems with various types of singularities.

This seminar presents a brief overview of with weight functional space of the Kudryavtsev type, called the space with multiweighted derivatives. In the first part of the talk, we will define space with multiweighted derivatives and consider the behavior of the function at the boundary of the investigated space. Following the ideas of L.D. Kudryavtsev, we will define the boundary values of a function and of its derivatives at the singular point. In addition, we will give necessary and sufficient conditions for weight functions in order that each function of the space is stabilized to some unique polynomial at zero, and will provide estimates for the rate of stabilization to a polynomial. Next, we will introduce functionals that depend on the boundary values at the singular point and that are equivalent to the norm of the space.

In the very last part of the talk, we will introduce necessary and sufficient conditions for weight functions so that continuous and compact embeddings between spaces of multiweighted derivatives hold. Moreover, we will show conditions on the weight functions in order that the inequality of the Nikol’skii-Lizorkin-Kudryatsev type is valid.

The video of the seminar will appear shortly afterwards in this Mediaspace channel.