Titlebook: Hardy Spaces on the Euclidean Space; Akihito Uchiyama Book 2001 Springer Japan 2001 Dimension.Hardy Spaces.bounded mean oscillation.maximu

全能

Operators on ,,,We introduce several important operators on .. and give easy estimates to them. As for the definitions of ., . and г(., δ) recall Section 0. Recall that {the volume of the unit ball in ..} = ..

adhesive

nurture

可商量

Hardy-Littlewood-Fefferman-Stein type inequalities, 1,Theorem 6.A . Let . ∈ {2,3,4, …} and . > 0. Let . (z) be a harmonic function defined on the unit ball of ... Then

CANE

易改变

Hardy-Littlewood-Fefferman-Stein type inequalities, 3,(You can skip this section if you are not interested in Section 10.) Theorem 8.1.

tympanometry

,Good λ inequalities for nontangential maximal functions and ,-functions of harmonic functions,For a harmonic function .) on .+., let .δ. be as in (0.2) and let.where ∇ = (..,…,..). We will show the following precise relations between .δ. and .δ (.|∇.|).

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A direct proof of ,,where . (In (12.3), .) denotes the Poisson kernel.) Since . dominates . by (10.19), (12.1) follows from Lemma 2.2 (with . = 1) and Theorem 2.2. In this section, we explain C. Fefferman’s direct proof of (12.1), which is one of the oldest proofs of his ..-BMO duality theorem. (Another one of the oldest proofs will be explained in Section 19.)

Negligible

A direct proof of,, where . is defined by (12.3) and . Since . dominates . by Theorems 4.1 and 9.3, we have already obtained (13.1). In this section, we give a direct proof of (13.1) by modifying the argument of L. Carleson [76] and by using the ideas in .. Th. Varopoulos [77], P. W. Jones [78] and J. B. Garnett-P. W. Jones [82].

CULP