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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

8 votes

Sets that project to zero measure on all lines except one

This can be done with an iterated Venetian blind construction. The idea is you start with a horizontal line segment, replace it with many small rotated parallel line segments, and repeat. In each step …
Alan C's user avatar
  • 613
8 votes
1 answer
652 views

Can this inequality be proved using weighted maximal function estimates?

I am trying to understand the following fact: Suppose $\{B_i\}_i$ are disjoint balls in $\mathbb R^n$, and $A_i \subset 100 B_i$ is a subset with $|A_i| \geq c |B_i|$. Then for any nonnegative $f$, w …
Alan C's user avatar
  • 613