Weak type estimates for cone type multipliers associated with a convex polygon

Sunggeum Hong, Joonil Kim, Chan Woo Yang

Research output: Contribution to journalArticle

Abstract

Let P be a convex polygon in ℝ2 which contains the origin in its interior. Let p be the associated Minkowski functional defined by ρ(ξ) = inf{ε > 0: ε-1 ξ ∈ P), ξ ≠ 0. We consider the family of convolution operators Tδ associated with cone type multipliers (1- ρ(ξ) 22)δ +, (ξ, τ) ∈ ℝ2 × ℝ, and show that Tδ is of weak type (p, p) on Hp (ℝ3), 1/2 < p < 1 for the critical value 5 = 2 (1 / p - 1).

Original languageEnglish
Pages (from-to)1827-1870
Number of pages44
JournalIndiana University Mathematics Journal
Volume56
Issue number4
DOIs
Publication statusPublished - 2007 Oct 29

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Convolution Operator
Convex polygon
Multiplier
Critical value
Interior
Cone
Estimate
Family

Keywords

  • Cone type multipliers
  • Convex polygons
  • Hardy spaces
  • Minkowski functional

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Weak type estimates for cone type multipliers associated with a convex polygon. / Hong, Sunggeum; Kim, Joonil; Yang, Chan Woo.

In: Indiana University Mathematics Journal, Vol. 56, No. 4, 29.10.2007, p. 1827-1870.

Research output: Contribution to journalArticle

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