Davis's inequality for orthogonal martingales under differential subordination.

Bañuelos, Rodrigo; Wang, Gang

doi:10.1307/mmj/1030374671

Cited by 18 publications

(12 citation statements)

References 14 publications

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“…[15] or Protter [20]. The condition that [M, M ] t − [N, N ] t is nonnegative and nondecreasing in t for t ≥ 0 was introduced and used by Bañuelos and Wang [3] and Wang [22]; see also [4], [5].…”

Section: Taking Expectations Of Both Sides Givesmentioning

confidence: 99%

A sharp weak type $(p,p)$ inequality $(p>2)$ for martingale transforms and other subordinate martingales

Suh

2004

Trans. Amer. Math. Soc.

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Abstract. If (dn) n≥0 is a martingale difference sequence, (εn) n≥0 a sequence of numbers in {1, −1}, and n a positive integer, thenHere αp denotes the best constant. If 1 ≤ p ≤ 2, then αp = 2/Γ(p + 1) as was shown by Burkholder. We show here that αp = p p−1 /2 for the case p > 2, and that p p−1 /2 is also the best constant in the analogous inequality for two martingales M and N indexed by [0, ∞), right continuous with limits from the left, adapted to the same filtration, and such that [M, M ]t −[N, N ]t is nonnegative and nondecreasing in t. In Section 7, we prove a similar inequality for harmonic functions.

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Section: Taking Expectations Of Both Sides Givesmentioning

confidence: 99%

A sharp weak type $(p,p)$ inequality $(p>2)$ for martingale transforms and other subordinate martingales

Suh

2004

Trans. Amer. Math. Soc.

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“…In Sect. 4 we prove that the constant β cannot be replaced in (1.3) by a smaller one. The final part of the paper contains the proofs of technical facts needed in the earlier considerations.…”

Section: Both Inequalities Are Sharp Even If H = Rmentioning

confidence: 78%

“…There are many other related results, see e.g., the papers [3] and [4] by Bañuelos and Wang, [11] and [13] by Burkholder and consult the references therein. For more recent works, we refer the interested reader to the papers [18][19][20] by the author, and [6,7] by Borichev et al The estimates have found numerous applications in many areas of mathematics, in particular, in the study of the boundedness of various classes of Fourier multipliers (consult, for instance, [1][2][3]12,16,17]).…”

Section: Both Inequalities Are Sharp Even If H = Rmentioning

confidence: 99%

Maximal Inequalities for Martingales and Their Differential Subordinates

̧kowski

2012

J Theor Probab

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“…In the proof of Theorem 2.2 we shall require the following auxiliary fact, which appears (in a slightly different form) as Corollary 1 in Bañuelos and Wang [4].…”

Section: (Ii) the Partial Derivative U λX X Is Nonpositive In The Intmentioning

confidence: 99%

Sharp weak type estimates for Riesz transforms

Oşekowski

2014

Monatsh Math

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Let d be a given positive integer and let {R j } d j=1 denote the collection of Riesz transforms on R d . For 1 < p < ∞, we determine the best constant C p such that the following holds. For any locally integrable function f on R d and any j ∈ {1, 2, . . . , d},A related statement for Riesz transforms on spheres is also established. The proofs exploit Gundy-Varopoulos representation of Riesz transforms and appropriate inequality for orthogonal martingales.

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Davis's inequality for orthogonal martingales under differential subordination.

Cited by 18 publications

References 14 publications

A sharp weak type $(p,p)$ inequality $(p>2)$ for martingale transforms and other subordinate martingales

A sharp weak type $(p,p)$ inequality $(p>2)$ for martingale transforms and other subordinate martingales

Maximal Inequalities for Martingales and Their Differential Subordinates

Sharp weak type estimates for Riesz transforms

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