关于非线性位势的Good- $λ$不等式
On the Good-$λ$ inequality for nonlinear potentials
摘要：
本文推广了B. Muckenhoupt和R.惠登从两个方面改进了经典结果。首先考虑了一般的非线性势，然后证明了不等式中的常数是指数衰减的。由此得到了一类拟线性椭圆型方程解的梯度的指数可积性。这反过来又是一个后果，某些Morrey空间嵌入扩展经典结果的里斯位势。此外，本文证明的良- $λ$不等式为Jawerth，Perez和Welland关于某些加权Triebel-Lizorkin空间中正锥的结果提供了一个初等证明.
英文摘要：
This note concerns an extension of the good-$λ$ inequality for fractional integrals, due to B. Muckenhoupt and R. Wheeden. The classical result is refined in two aspects. Firstly, general nonlinear potentials are considered; and secondly, the constant in the inequality is proven to decay exponentially. As a consequence, the exponential integrability of the gradient of solutions to certain quasilinear elliptic equations is deduced. This in turn is a consequence of certain Morrey space embeddings which extend classical results for the Riesz potential. In addition, the good-$λ$ inequality proved here provides an elementary proof of the result of Jawerth, Perez and Welland regarding the positive cone in certain weighted Triebel-Lizorkin spaces.
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