Representability of some cones in weighted Lebesgue spaces and the extrapolation of operators on cones

• In this paper, for the most important cones in Lebesgue spaces, we propose reducing the problem of an estimate for an operator on a cone to the problem of an estimate for an operator on a new space, which is obtained constructively from the cone and the original space. Such a reduction makes it possible to apply the entire apparatus developed for obtaining sharp estimates on weighted Lebesgue spaces to obtain sharp estimates for operators on cones. Using this reduction, we also state, for a certain class of operators, a new theorem on the extrapolation of operators defined on cones in Lebesgue spaces.

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Mathematics

Matematik

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)