1,077 research outputs found
The Daugavet property in the Musielak-Orlicz spaces
We show that among all Musielak-Orlicz function spaces on a -finite
non-atomic complete measure space equipped with either the Luxemburg norm or
the Orlicz norm the only spaces with the Daugavet property are ,
, and . We
obtain in particular complete characterizations of the Daugavet property in the
weighted interpolation spaces, the variable exponent Lebesgue spaces (Nakano
spaces) and the Orlicz spaces.Comment: 20 page
New examples of K-monotone weighted Banach couples
Some new examples of K-monotone couples of the type (X, X(w)), where X is a
symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on
the property of the w-decomposability of a symmetric space we show that, if a
weight w changes sufficiently fast, all symmetric spaces X with non-trivial
Boyd indices such that the Banach couple (X, X(w)) is K-monotone belong to the
class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental
function of X is t^{1/p} for some p \in [1, \infty], then X = L_p. At the same
time a Banach couple (X, X(w)) may be K-monotone for some non-trivial w in the
case when X is not ultrasymmetric. In each of the cases where X is a Lorentz,
Marcinkiewicz or Orlicz space we have found conditions which guarantee that (X,
X(w)) is K-monotone.Comment: 31 page
New Real-Variable Characterizations of Musielak-Orlicz Hardy Spaces
Let be such that
is an Orlicz function and is a
Muckenhoupt weight. The Musielak-Orlicz Hardy space
is defined to be the space of all such that the grand maximal function belongs to the
Musielak-Orlicz space . Luong Dang Ky established its
atomic characterization. In this paper, the authors establish some new
real-variable characterizations of in terms of the
vertical or the non-tangential maximal functions, or the Littlewood-Paley
-function or -function, via first establishing a
Musielak-Orlicz Fefferman-Stein vector-valued inequality. Moreover, the range
of in the -function characterization of
coincides with the known best results, when
is the classical Hardy space , with
, or its weighted variant.Comment: J. Math. Anal. Appl. (to appear
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