Jump and variational inequalities for averaging operators with variable kernels
Jump and variational inequalities for averaging operators with variable kernels
In this paper, we prove that the jump function and variation of averaging operators with rough variable kernels are bounded on $ L^{2}(\mathbb{R}^{n}) $ if $ \Omega\in L^{\infty}(\mathbb{R}^{n})\times L^{q}(\mathbb{S}^{n-1}) $ for $ q>2(n-1)/n $ and $ n\geq2 $. Moreover, we obtain the boundedness on weighted $ L^{p}(\mathbb{R}^{n}) $ spaces of …