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The wavelet characterization of the space Weak H¹

100%

Liu H.

Studia Mathematica

1992

tom 103

nr 1

109-117

The space Weak H¹ was introduced and investigated by Fefferman and Soria. In this paper we characterize it in terms of wavelets. Equivalence of four conditions is proved.

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

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.

Ograniczanie wyników

2 Studia Mathematica

2 Liu H.

1 Lin C.-C.

1 Lin Y.-C.

1 Liu Y.

1 2011

1 1992

Wyniki wyszukiwania

The wavelet characterization of the space Weak H¹

Bilinear operators associated with Schrödinger operators