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1
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Convolution operators on Hardy spaces

100%
Lin C.-C.
Studia Mathematica
|
1996
|
tom 120
|
nr 1
53-59
EN
We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces $H^p(G)$, where G is a homogeneous group.
2
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Almost everywhere convergence of Laguerre series

64%
Chen C.-P., Lin C.-C.
Studia Mathematica
|
1994
|
tom 109
|
nr 3
291-301
EN
Let $a ∈ ℤ^+$ and $f ∈ L^p (ℝ^+), 1 ≤ p ≤ ∞ $. Denote by $c_j$ the inner product of f and the Laguerre function $ℒ^a_j$. We prove that if ${c_j}$ satisfies $lim_{λ↓1} \overline lim_{n→∞} ∑_{n
3
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Calderón-Zygmund operators acting on generalized Carleson measure spaces

64%
Lin C.-C., Wang K.
Studia Mathematica
|
2012
|
tom 211
|
nr 3
231-240
EN
We study Calderón-Zygmund operators acting on generalized Carleson measure spaces $CMO^{α,q}_{r}$ and show a necessary and sufficient condition for their boundedness. The spaces $CMO^{α,q}_{r}$ are a generalization of BMO, and can be regarded as the duals of homogeneous Triebel-Lizorkin spaces as well.
4
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The continuity of pseudo-differential operators on weighted local Hardy spaces

51%
Lee M.-Y., Lin C.-C., Lin Y.-C.
Studia Mathematica
|
2010
|
tom 198
|
nr 1
69-77
EN
We first show that a linear operator which is bounded on $L²_{w}$ with w ∈ A₁ can be extended to a bounded operator on the weighted local Hardy space $h¹_{w}$ if and only if this operator is uniformly bounded on all $h¹_{w}$-atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to $h¹_{w}$.
5
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Bilinear operators associated with Schrödinger operators

51%
Lin C.-C., Lin Y.-C., Liu H., Liu Y.
Studia Mathematica
|
2011
|
tom 205
|
nr 3
281-295
EN
Let L = -Δ + V be a Schrödinger operator in $ℝ^{d}$ and $H¹_L(ℝ^{d})$ be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by $T^{±}(f,g)(x) = (T₁f)(x)(T₂g)(x) ± (T₂f)(x)(T₁g)(x)$, where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from $L^{p}(ℝ^{d}) × L^{q}(ℝ^{d})$ to $H¹_L(ℝ^{d})$ for 1 < p,q < ∞ with 1/p + 1/q = 1. Several examples satisfying these conditions are given. We also give a counterexample for which the classical Hardy space estimate fails.
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