By Maxime Bocher

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**Additional resources for An Introduction to the Study of Integral Equations**

**Example text**

5 the definition of does not depend on the paratlas on F. Indeed, ticular choice of the could equivalently be defined as the linear space of functions n = uI r with is c u=0 on 8S2\P. r = 0). H). We leave the details to the reader. 3. Lebesgue Spaces We assume that the reader is familiar with the basic theory of Lebesgue measure and integral, such as can be found, for instance in W. Rudin [133]. a. , respectively, for "almost any" and "almost 17 Function Spaces everywhere" with respect to Lebesgue measure measx on RN.

2, u> =

Then there exists fe LP'(S2), with I f Ip':o = I F I(e°cmr', such that

r; Chapter 1 20 the definition of p * u is trivially extended to the whole of S5 if dist(supp u, OQ) > 2r.