# Real Analysis

Real analysis is the modern generalization of differential and integral calculus. This tag contains posts on calculus, measure theory, geometry and topology of Euclidean spaces.

### A Weighted/Interpolated Young's Inequality

A follow up to my previous post on Young's inequality.

### The Translation Action on Function Spaces

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …

### Some Periodic Functions

Some non-intuitive facts about periodic functions

### An Elementary Proof of Young's Inequality

A proof of a generalized form of Young's inequality is given without the need of interpolation theory.

### Joris' Theorem

A proof is given of Joris' theorem, which states that if two coprime powers of a function are both smooth, then so is the original …

### A Better Estimate of Kempner's Series

The Kempner series recently regained some notoriety due to a Saturday Morning Breakfast Cereal comic (the last panel). The observation …

### Bessaga's converse to the contraction mapping theorem

A converse to Banach's fixed point theorem, due to Bessaga, is discussed.

### Approximating Continuous Functions

Expository note on the Runge phenomenon

### Mariş's Theorem

We describe a theorem due to Mihai Mariş concerning the symmetries of ground states.