The direct and inverse approximation theorems in metrics of the global Morrey-type space
Keywords:
Morrey space, direct approximation theorem, inverse approximation theoremAbstract
In recent years, number of research works in the theory of the general Morrey type spaces
are increased. The Morrey space was originally introduced by C. Morrey in 1938 to study the
local properties of solutions of elliptic equations. Then theory of the Morrey spaces continued
to develop at its own discretion and found wide application in functional analysis, theory of
partial differential equations. In this paper we consider the global Morrey type spaces in terms
of approximation theory. At the beginning of this work we take a short journey into the history
of such important section of approximation theory as direct approximation theorem, also known
as Jackson’s inequality, and inverse approximation theorem. For functions from this spaces there
are proved the analogue of the Minkowski inequality and analogue of the Bernstein inequality.
Further, exploiting them and entire functions of exponential type, we obtain the direct and inverse
approximation theorems in metrics of the global Morrey-type space and show that the degree of
approximation depends on differential properties of function.
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