It is proved that
given $-1/2<s<1/2$, for any $f\in L^2(\mathbb{R})$, there is a unique $u\in \widehat{H}^{|s|}(\mathbb{R})$ such that $$ f=\boldsymbol{D}^{-s}u+\boldsymbol{D}^{s*}u\,, $$ where $\boldsymbol{D}^{-s}, \boldsymbol{D}^{s*}$ are fractional Riemann-Liouville operators and the fractional derivatives are understood in the weak sense. Furthermore, the regularity of $u$ is discussed, and other versions of the results are established. As an interesting consequence, the Fourier transform… Expand

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures… Expand

Download PDF Ebook and Read OnlineAn Introduction To Sobolev Spaces And Interpolation Spaces%0D. Get An Introduction To Sobolev Spaces And Interpolation Spaces%0D An Introduction to Sobolev Spaces… Expand

THE appearance of these volumes marks the happy conclusion of a work undertaken, as the author reminds us in his preface, twenty-one years ago. Doubtless it would have been finished earlier had it… Expand