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(This is essentially a continuation of my previous question, here.) Let $(X,d,\mu)$ be a metric measure space, i.e. $\mu$ is a Borel measure on the metric space $(X,d)$. Further assume (though you ...

Let $(X,d,\mu)$ be a metric measure space, i.e. $\mu$ is a Borel measure on the metric space $(X,d)$. I'll denote the Hardy-Littlewood maximal operator - either centred or uncentred, I don't mind ...

I am reading Terence Tao's paper "A sharp bilinear restriction estimate for paraboloids" to prove the bilinear restriction estimate on paraboloids. In Section 3, he assumes that $\text{diam}(...