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Directors:
Randolph E. Bank
Philip E. Gill
Michael Holst

Terry Le

Office: AP&M 7431
Phone: (858)534-9813
Fax: (858)534-5273
E-mail: tele@ucsd.edu
Pointwise Multiplication in Bessel Potential Spaces and Sobolev-Slobodeckij Spaces

Let $f \in W^{s1,p1}$ and $g \in W^{s2,p2}$ ($s1,s2\ge 0)$. What can be said about $fg$? To which Sobolev spaces does the product $fg$ belong? This is the question that we want to talk about. Why do we care about this question? As we will discuss, one of the main applications of such results is in the theory of partial differential equations (PDEs) and in particular nonlinear elliptic PDEs. We will review some of the well-known results and present alternate proofs of those results. In particular we will point out a common mistake in some of the existing literature as we discuss the question of existence of Holder-type inequalities for the product of two functions in Sobolev spaces.