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
Y1 - 2007
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
UR - http://www.scopus.com/inward/record.url?scp=35448962904&partnerID=8YFLogxK
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
AN - SCOPUS:35448962904
VL - 56
SP - 1827
EP - 1870
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
SN - 0022-2518
IS - 4
ER -