Theory of Hp Spaces

By Peter L. Duren. 2000

1,616 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7991403f342854217af573384ebc80be0cebf826

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Citations in the corpus

Boundedness of the Bergman projection on $L^p$ spaces with exponential weights (2013, result): “k for the Hadamard product of WΦ n and f. With this notation we can state the next result, which follows from the considerations in [13, p.111-113]. We denote by Hpthe classical Hardy spaces on D(see [6]). Theorem A. Let Φ : R→ C be a C∞-function with compact support supp(Φ). The following assertion”
Division by Flat Ultradifferentiable Functions and Sectorial Extensions (2003, neutral): “[8], theorem 11.”
Two weight inequalities for individual Haar multipliers and other well localized operators (2007, methodology): “re condition (3.3) X Q⊂R a Q ≤ µ(R), then for any f ∈ L2(µ) X R∈D a R |f R |2 ≤ Ckfk2 L2(µ) where C is an absolute constant. 12 F. NAZAROV, S. TREIL AND A. VOLBERG This theorem is very well known, cf [Dur70]. For an alternative prove see also [NTV], [NT], [NTV3], where it was proved with the constan”
Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics (2005, methodology): “Given Lemma 8.5, standard H 2 theory [36, 13 , 24] implies that”
An equivalence for weighted integrals of an analytic function and ist derivative (2008, methodology): “The first of them is well known and is due to Hardy and Littlewood, (see the proof of Theorem 5.5 of [ 3 ]).”
The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals (2005, background): “th t1/2p′ replaced by t1/p′); this corresponds to setting ψ(x) = 1 π(1+x2) , which is not log-concave. In this regard, it is a classical result, essentially due to Hardy and Littlewood [HL] (see also [D], Theorem 5.9) that if p ≥ 1, then t1/p′kφ(·,t)k p is bounded as a function of s, and in fact it ”
INTEGRABILITY OF THE DERIVATIVE OF A BLASCHKE PRODUCT (2007, methodology): “improved (see Theorem 5.6 of [ 13 ] and [24] or [34] for a simple proof).”
Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls (2007, background): “We refer to [1] and [18] for the basic theory of these spaces.”
Inner functions on the bidisk and associated Hilbert spaces (2012, background): “has no zeros on D2, and therefore both f(·,z2) and 1/p(·,z2) are in the Smirnov class N+ for a.e. z2 ∈ T. As N+ is an algebra, f(·,z 2)/p(·,z2) is in N+ for a.e. z2 ∈ T. Since N+ ∩ L2(T) = H2(T) (see [14]), f(·,z 2)/p(·,z2) ∈ H2(T) for a.e. z2 ∈ T. This implies f/p⊥ L2 −•. A similar argument shows f”
A new class of operators and a description of adjoints of composition operators (2006, background): “It is well known (see [6], for instance) that for any two Hardy functions f and g, the inner product in H 2(D), denoted by 〈f,g〉H 2(D), can be computed by means of an integral of their boundary values”
Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type (2008, background): “Minkowski’s inequality in its integral form (see [4,8]), followed by a change of variable x−1 = u and some simple estimates yields”