Abstract:
The article describes the process of getting estimations of norms of derivatives of Dirichlet $\Lambda$-kernels for $D_{Q(\Lambda,N)}(x)$ in $L^p$ by when the spectrum lies in approximating polynomials sets the type of hyperbolic crosses.
Keywords:multi-dimensional Dirichlet kernel with an arbitrary spectrum, $(r,a)$-derivative of function, hyperbolic crosses.