Speaker
Description
Green functions are very interesting from different aspects and are used
for solving wide variety of problems in many fields, specifically in
quantum field theory, aerodynamics, aeroacoustics, electrodynamics and
seismology. Considering Green functions, we obtain new results on the
Hardy-type inequality in the general context, in terms of measure spaces
with positive $\sigma$-finite measures. We investigate the difference
operator derived from the Hardy-type inequality on the one hand and the
expression containing the interpolating polynomial of Abel-Gontscharoff
and the four Green functions on the other hand and make connections
between them. We discuss the n-convexity of the function and consider
the result depending on the parity of the indexes. Further, we present
results obtained by using the H\" older inequality for conjugate
exponents $p$ and $q$. Finally, we conclude with upper bounds for the
remainder, obtained from the main result, using the Čebyšev
functional.
