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Weak and Strong Type ... formula ...–... formula ... Estimates for Sparsely Dominated Operators

机译：弱强类型...公式... – ...公式...稀疏控制算子的估计

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摘要

We consider operators T satisfying a sparse domination property

\begin{matrix} | ⟨ T f, g ⟩ | \leq c \sum_{Q \in S} {⟨ f ⟩}_{p_{0}, Q} {⟨ g ⟩}_{q_{0}^{'}, Q} | Q | \end{matrix}

with averaging exponents

1 \leq p_{0} < q_{0} \leq \infty

. We prove weighted strong type boundedness for

p_{0} < p < q_{0}

and use new techniques to prove weighted weak type

(p_{0}, p_{0})

boundedness with quantitative mixed

A_{1}

–

A_{\infty}

estimates, generalizing results of Lerner, Ombrosi, and Pérez and Hytönen and Pérez. Even in the case

p_{0} = 1

we improve upon their results as we do not make use of a Hörmander condition of the operator T. Moreover, we also establish a dual weak type

(q_{0}^{'}, q_{0}^{'})

estimate. In a last part, we give a result on the optimality of the weighted strong type bounds including those previously obtained by Bernicot, Frey, and Petermichl.

机译：我们认为运算符T满足稀疏的控制属性

\begin{matrix} |⟨Tf，g⟩< mo Stretchy =“ false”> |\leqc\sumQ\inS⟨f⟩p0< / msub>，Q⟨g⟩q0'，Q|Q < / mi>|，平均指数为 \end{matrix}

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期刊名称 Springer Open Choice
作者
Dorothee Frey; Bas Nieraeth;
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作者单位

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年(卷),期 -1(29),1
年度 -1
页码 247–282
总页数 36
原文格式 PDF
正文语种
中图分类外科学;
关键词
Sparse domination Muckenhoupt weights Sharp weighted bounds;

机译：稀疏统治;Mukenhoupt权重;夏普加权边界;

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1. Weak and Strong Type A(1)-A(infinity) Estimates for Sparsely Dominated Operators [J] . Frey Dorothee, Nieraeth Bas The Journal of geometric analysis . 2019,第1期

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2. On a Weak Type Estimate for Sparse Operators of Strong Type [J] . Karagulyan G. A., Mnatsakanyan G. Journal of Contemporary Mathematical Analysis . 2019,第4期

机译：强类型的稀疏算子的弱类型估计
3. THE $L_{r}$ CONVERGENCE AND WEAK LAWS OF LARGE NUMBERS FOR $widetilde{unicode[STIX]{x1D70C}}$ -MIXING RANDOM VARIABLES [J] . YAN-JIAO MENG The ANZIAM journal: the Australian & New Zealand industrial and applied mathematics journal . 2017,第3a4期

机译： $ L_ {r} $ $ widetilde { unicode [STIX] {x1D70C}} $$ -混合随机变量
4. STRONG TYPE ESTIMATION FROM WEAK TYPE ESTIMATES FOR SOME INTEGRAL OPERATORS [C] . Nobuhiko FUJII ISAAC congress . 2000

机译：一些积分算子的弱型估计的强类型估计
5. A Different Approach to Endpoint Weak-Type Estimates for Calderón-Zygmund Operators [D] . Stockdale, Cody B. 2020

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6. Blending type approximation by ... formula ... operators of bivariate tensor product of λ-Bernstein–Kantorovich type [O] . Qing-Bo Cai, Guorong Zhou -1

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7. Sharp off-diagonal weighted weak type estimates for sparse operators [O] . Qian un He, Dun an Yan 2020

机译：稀疏运算符的尖锐非对角线加权弱型估计

Weak and Strong Type ... formula ...–... formula ... Estimates for Sparsely Dominated Operators

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