4 citations · 4 across the 3 of their papers we have counts for
4 papers · 1 filter
On the constants for multiplication in Sobolev spaces
Carlo Morosi, Livio Pizzocchero
For n > d/2, the Sobolev (Bessel potential) space H^n(R^d, C) is known to be a Banach algebra with its standard norm || ||_n and the pointwise product; so, there is a best constant…
Quantitative functional calculus in Sobolev spaces
Carlo Morosi, Livio Pizzocchero
In the framework of Sobolev (Bessel potential) spaces $H^n(\reali^d, \reali {or} \complessi)$, we consider the nonlinear Nemytskij operator sending a function $x \in \reali^d \maps…
On the constants in some inequalities for the Sobolev norms and pointwise product
C. Morosi, L. Pizzocchero
We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.
On the constants for some Sobolev imbeddings
C. Morosi, L. Pizzocchero
We consider the imbedding inequality || f ||_{L^r(R^d)} <= S_{r,n,d} || f ||_{H^{n}(R^d)}; H^{n}(R^d) is the Sobolev space (or Bessel potential space) of L^2 type and (integer or f…