论文标题
锥，可纠正性和奇异整体操作员
Cones, rectifiability, and singular integral operators
论文作者
论文摘要
令$μ$为$ \ mathbb {r}^d $的ra度量。我们定义和研究锥形能量$ \ MATHCAL {e} _ {μ，p}（x，v，α）$，它量化了用顶点$ x \ in \ mathbb {r}^d $，in g（d，d-n）$和aperture的$ x \ in \ mathbb {r}^d $ v \ in \ mathbb {r}^d $ v \ in（0）的$ x $ x \ in cone的部分。我们使用这些能量来表征可重差性和Lipschitz图形属性的大量。此外，如果我们假设$μ$具有多项式生长，则为$ l^2（μ）$ - 具有卷积类型奇数奇数的单数积分算子的界限提供了足够的条件。
Let $μ$ be a Radon measure on $\mathbb{R}^d$. We define and study conical energies $\mathcal{E}_{μ,p}(x,V,α)$, which quantify the portion of $μ$ lying in the cone with vertex $x\in\mathbb{R}^d$, direction $V\in G(d,d-n)$, and aperture $α\in (0,1)$. We use these energies to characterize rectifiability and the big pieces of Lipschitz graphs property. Furthermore, if we assume that $μ$ has polynomial growth, we give a sufficient condition for $L^2(μ)$-boundedness of singular integral operators with smooth odd kernels of convolution type.
