We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving mutations between fake weighted projective spaces are mutations over edges of the corresponding simplices. As an application, we analyse the canonical and terminal fake weighted projective s...

We investigate the Cohomological Crepant Resolution Conjecture for reduced Gorenstein weighted projective spaces. Using toric methods, we prove this conjecture in some new cases. As an intermediate step, we show that weighted projective spaces are toric Deligne-Mumford stacks. We also describe a combinatorial model for the orbifold cohomology of weighted projective spaces.

We give short simple proofs of Uspenskii’s results characterizing Besov spaces as trace spaces of weighted Sobolev spaces. We generalize Uspenskii’s results and prove the optimality of these generalizations. We next show how classical results on the functional calculus in the Besov spaces can be obtained as straightforward consequences of the theory of weighted Sobolev spaces.

Action of p ? on distributions is examined in the context of Sobolev spaces, weighted L 2 spaces and weighted Sobolev spaces, respectively. The results obtained are as follows: Let k be a real number. (1) If f is in H

We investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H∞. Applications for composition operators on weighted Bloch spaces are given.