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Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

100%

Liu L., Yang D.

Studia Mathematica

2009

tom 190

nr 2

163-183

Let s ∈ ℝ, p ∈ (0,1] and q ∈ [p,∞). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space $Ḟ^{s}_{p,q}(ℝⁿ)$ to a quasi-Banach space ℬ if and only if sup{$||T(a)||_{ℬ}$: a is an infinitely differentiable (p,q,s)-atom of $Ḟ_{p,q}^{s}(ℝⁿ)$} < ∞, where the (p,q,s)-atom of $Ḟ_{p,q}^{s}(ℝⁿ)$ is as defined by Han, Paluszyński and Weiss.

Multilinear analysis on metric spaces

87%

Grafakos L., Liu L., Maldonado D., Yang D.

Instytut Matematyczny Polskiej Akademii Nauk

The multilinear Calderón-Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón-Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel-Lizorkin spaces in the full range of exponents are among the main results obtained. Multilinear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces, and Triebel-Lizorkin spaces are also proved. Applications include the boundedness of paraproducts and bilinear multiplier operators on products of Besov and Triebel-Lizorkin spaces.

Ograniczanie wyników

1 Studia Mathematica

2 Liu L.

2 Yang D.

1 Grafakos L.

1 Maldonado D.

1 2014

1 2009

Wyniki wyszukiwania

Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Multilinear analysis on metric spaces