Matemáticahttps://hdl.handle.net/10669/2802023-09-23T13:53:29Z2023-09-23T13:53:29ZOn the supremum of a family of set functionshttps://hdl.handle.net/10669/899552023-09-08T20:55:26Z2023-01-01T00:00:00ZOn the supremum of a family of set functions
The concept of supremum of a family of set functions was introduced by M. Veraar and I. Yaroslavtsev (2016) for families of measures defined on a measurable space. We expand this concept to include families of set functions in a very general setting. The case of families of signed measures is widely discussed and exploited.
2023-01-01T00:00:00ZQuadratic variation for cylindrical martingale-valued measureshttps://hdl.handle.net/10669/899532023-09-08T19:54:11Z2023-01-01T00:00:00ZQuadratic variation for cylindrical martingale-valued measures
This article focuses in the definition of a quadratic variation for cylindrical orthogonal martingale-valued measures defined on Banach spaces. Sufficient and necessary conditions for the existence of such a quadratic variation are provided. Moreover, several properties of the quadratic variation are explored, as the existence of a quadratic variation operator. Our results are illustrated with numerous examples and in the case of a separable Hilbert space, we delve into the relationship between our definition of quadratic variation and the intensity measures defined by Walsh (1986) for orthogonal martingale measures with values in separable Hilbert spaces. We finalize with a construction of a quadratic covariation and we explore some of its properties.
2023-01-01T00:00:00ZThe Sparse T1 Theorem [presentación]https://hdl.handle.net/10669/899512023-09-08T19:34:35Z2017-03-01T00:00:00ZThe Sparse T1 Theorem [presentación]
Presentación de diapositivas
2017-03-01T00:00:00ZLacunary discrete spherical maximal functionshttps://hdl.handle.net/10669/899472023-09-07T15:21:11Z2019-01-01T00:00:00ZLacunary discrete spherical maximal functions
We prove new l^p(Z^d) bounds for discrete spherical averages in dimensions d greater than or equal to 5. We focus on the case of lacunary radii, first for
general lacunary radii, and then for certain kinds of highly composite
choices of radii. In particular, if Aλf is the spherical average of f over
the discrete sphere of radius λ, we have for any lacunary sets of integers {λ
2
k}. We follow a style of argument
from our prior paper, addressing the full supremum. The relevant maximal operator is decomposed into several parts; each part requires only
one endpoint estimate.
2019-01-01T00:00:00Z