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) 2/τ2)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 language | English |
|---|---|
| Pages (from-to) | 1827-1870 |
| Number of pages | 44 |
| Journal | Indiana University Mathematics Journal |
| Volume | 56 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2007 Oct 29 |
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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 journal › Article
}
TY - JOUR
T1 - Weak type estimates for cone type multipliers associated with a convex polygon
AU - Hong, Sunggeum
AU - Kim, Joonil
AU - Yang, Chan Woo
PY - 2007/10/29
Y1 - 2007/10/29
N2 - 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) 2/τ2)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).
AB - 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) 2/τ2)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).
KW - Cone type multipliers
KW - Convex polygons
KW - Hardy spaces
KW - Minkowski functional
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UR - http://www.scopus.com/inward/citedby.url?scp=35448962904&partnerID=8YFLogxK
U2 - 10.1512/iumj.2007.56.2946
DO - 10.1512/iumj.2007.56.2946
M3 - Article
VL - 56
SP - 1827
EP - 1870
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
SN - 0022-2518
IS - 4
ER -