2 results
ON STATISTICAL PROPERTIES OF NONLINEAR FUNCTIONALS OF RANDOM FIELDS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 103 / Issue 2 / April 2021
- Published online by Cambridge University Press:
- 18 September 2020, pp. 338-340
- Print publication:
- April 2021
-
- Article
-
- You have access
- Export citation
Embeddings of homogeneous Sobolev spaces on the entire space
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 1 / February 2021
- Published online by Cambridge University Press:
- 09 March 2020, pp. 296-328
- Print publication:
- February 2021
-
- Article
- Export citation
-
We completely characterize the validity of the inequality
$\| u \|_{Y(\mathbb R)} \leq C \| \nabla^{m} u \|_{X(\mathbb R)}$, where X and Y are rearrangement-invariant spaces, by reducing it to a considerably simpler one-dimensional inequality. Furthermore, we fully describe the optimal rearrangement-invariant space on either side of the inequality when the space on the other side is fixed. We also solve the same problem within the environment in which the competing spaces are Orlicz spaces. A variety of examples involving customary function spaces suitable for applications is also provided.
