A characterization of the Morrey-Campanato spaces

Abstract

In this paper, we give a new characterization of the Morrey-Campanato spaces by using the convolution ϕ t B * f (x) to replace the minimizing polynomial P B f of a function f in the Morrey-Campanato norm, where ϕ ∈ S(R n ) is an appropriate Schwartz function. (2000): 42B35, 47G10 Mathematics Subject Classification

Old and New Morrey Spaces with Heat Kernel Bounds

“…The purpose of this article is twofold. First, we explore some new characterizations of L p,λ (R n ) through the fact that L p,λ (R n ) consists of all locally integrable complex-valued functions f on R n satisfying The second aim is to use those new characterizations as motives of a continuous study of [1,7,5,9] and so to introduce new Morrey spaces L p,λ L (R n ) associated with operators. Roughly speaking, if L is the infinitesimal generator of an analytic semigroup {e −tL } t≥0 on L 2 (R n ) with kernel p t (x, y) which decays fast enough, then we can view P t f = e −tL f as an average version of f at the scale t and use the quantity…”

Some characterizations for weighted Morrey‐Campanato spaces

“…Our next proof follows from [4] and [5]. We now introduce our new weighted Morrey-Campanoto type space L ϕ (β, ω) for β > 0.…”

Classes of Hardy spaces associated with operators, duality theorem and applications

“…See Definition 3.1 below. Note that the spaces H p √ (R n ) and L √ (α, 2, s) coincide with the classical H p (R n ) and the Morrey-Campanato spaces L(α, 2, s) (= Λ nα (R n ) of Lipschitz), respectively (Section 3 of [13]). (ii) As in [5], we give a molecular decomposition for function f in the H p L (R n ) spaces by using certain estimates on area integrals and tent spaces (see Proposition 3.3).…”

“…For more properties of the space H 1 L (R n ) and the BMO L (R n ) space, we refer the reader to [5], [17], [18], [13] and [12].…”