New abstract Hardy spaces
Copyright policy )New abstract Hardy spaces
The aim of this paper is to propose an abstract construction of spaces which keep the main properties of the (already known) Hardy spaces H^1. We construct spaces through an atomic (or molecular) decomposition. We prove some results about continuity from these spaces into L^1 and some results about interpolation between these spaces and the Lebesgue spaces. We also obtain some results on weighted norm inequalities. Then we apply this abstract theory to the L^p maximal regularity. Finally we present partial results in order to understand a characterization of the duals of Hardy spaces.
53 pages
- Ministry of Education (Malaysia)
- University Paris-Sud France
- Ministry of Education Portugal
- Neijiang Normal University China (People's Republic of)
- Ministry of Education Libyan Arab Jamahiriya
46M35, dual space, Hardy spaces, 42B25; 42B30; 42B35; 46M35, Hardy space, \(H^p\)-spaces, interpolation, Interpolation, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, atomic and molecular decomposition, Mathematics - Analysis of PDEs, FOS: Mathematics, Atomic and molecular decomposition, 42B30, Function spaces arising in harmonic analysis, Abstract harmonic analysis, a space of homogeneous type, 42B25, Analysis, 42B35, Analysis of PDEs (math.AP)
46M35, dual space, Hardy spaces, 42B25; 42B30; 42B35; 46M35, Hardy space, \(H^p\)-spaces, interpolation, Interpolation, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, atomic and molecular decomposition, Mathematics - Analysis of PDEs, FOS: Mathematics, Atomic and molecular decomposition, 42B30, Function spaces arising in harmonic analysis, Abstract harmonic analysis, a space of homogeneous type, 42B25, Analysis, 42B35, Analysis of PDEs (math.AP)
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