Local atomic decompositions for multidimensional Hardy spaces

2018/10/16 by Kania, Edyta, Plewa, Paweł, Preisner, Marcin
#33C45 #35J10 #42B25 #42B30 (primary) #47D03 (secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1810.06937

Abstract

We consider a nonnegative self-adjoint operator L on L²(X), where X⊆ ℝ^d. Under certain assumptions, we prove atomic characterizations of the Hardy space H¹(L) = ł\f∈ L¹(X) : ‖sup_t>0 |exp(-tL)f | ‖_L¹(X)

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