Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Παναγιωτάκος Νικόλαος
Supervisors info:
Αποστόλης Γιαννόπουλος Καθηγητής
Original Title:
Εκτιμήσεις για μεγιστικούς τελεστές που ορίζονται από κυρτά σώματα
Translated title:
High dimensional maximal functions associated to convex bodies
Summary:
The purpose of this dissertation is to estimate the norms of the maximal
operator difined by convex bodies. Firstly, some estimates are given for
the maximal operator difined by the n-dimensional euclidian ball, and
then these estimates are generalized for random convex bodies. The
general ambition is to achieve good results for high dimension and, when
possible, to get fragments independent of the dimension. Finally, the
cases of the L_q balls particularly are investigated and especially the
case of the n-dimensional cube.
Keywords:
Maximal operator, Maximal function, Estimates, Convex bodies, Harmonic Analysis
