Sharp growth estimates for dyadic $b$-input $T(b)$ theorems

Salomone, Stephanie

doi:10.5565/publmat_52208_02

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Introduction1

Definitions and Notation1

Proposition 21 (Nesting Property Of Dyadic Intervals)1

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2010

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“…In effect, this changes the theorem from a b-input case (where T is evaluated at a function b) to a b-output case, where T * (1) is evaluated by a norm which depends on b. This is a natural extension of the previous work, in particular in [2] where the dyadic T (b) theorems are proven and in [13], where sharp growth bounds for b-input theorems are proven. Our approach utilizes b-adapted Haar wavelets as in [5].…”

Section: Introductionmentioning

confidence: 66%

“…We use the same conventions as in [13]. For a more detailed explanation of these preliminaries, see [13,Section 2]. We consider the real line R decomposed into dyadic intervals, I.…”

Section: Definitions and Notationmentioning

confidence: 99%

“…As in [2,13], we restrict ourselves to a finite set of dyadic intervals on the half-line. We fix a large M , and let…”

Section: Proposition 21 (Nesting Property Of Dyadic Intervals)mentioning

confidence: 99%

See 2 more Smart Citations

b-weighted dyadic BMO from dyadic BMO and associatedT(b) theorems

Salomone

2010

Collect. Math.

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Given a function b, and using adapted Haar wavelets, we define a BMO-type norm which is dependent on b. In both global and local cases, we find the dependence of the bounds on f BMO by the bounds on the b-weighted BMO norm of f . We show that the dependence is sharp in the global case. Multiscale analysis is used in the local case. We formulate as corollaries global and local dyadic T (b) theorems whose hypotheses include a bound on the b-weighted BMO-norm of T * (1).

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Section: Introductionmentioning

confidence: 66%

“…We use the same conventions as in [13]. For a more detailed explanation of these preliminaries, see [13,Section 2]. We consider the real line R decomposed into dyadic intervals, I.…”

Section: Definitions and Notationmentioning

confidence: 99%