Corpus ID: 202565958

$L^p\to L^q$ bounds for spherical maximal operators

@article{Anderson2019LptoLB,
  title={\$L^p\to L^q\$ bounds for spherical maximal operators},
  author={T. Anderson and K. Hughes and J. Roos and A. Seeger},
  journal={arXiv: Classical Analysis and ODEs},
  year={2019}
}
  • T. Anderson, K. Hughes, +1 author A. Seeger
  • Published 2019
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • Let $f\in L^p(\mathbb{R}^d)$, $d\ge 3$, and let $A_t f(x)$ the average of $f$ over the sphere with radius $t$ centered at $x$. For a subset $E$ of $[1,2]$ we prove close to sharp $L^p\to L^q$ estimates for the maximal function $\sup_{t\in E} |A_t f|$. A new feature is the dependence of the results on both the upper Minkowski dimension of $E$ and the Assouad dimension of $E$. The result can be applied to prove sparse domination bounds for a related global spherical maximal function. 
    3 Citations

    Figures from this paper

    Assouad dimension and fractal geometry
    • 15
    • PDF
    Multi-scale sparse domination
    • 2
    • PDF

    References

    SHOWING 1-10 OF 33 REFERENCES
    Endpoint mapping properties of spherical maximal operators
    • 32
    • PDF
    Spherical maximal functions and fractal dimensions of dilation sets
    • 6
    • PDF
    Sparse Bounds for Spherical Maximal Functions
    • 38
    • Highly Influential
    • PDF
    New dimension spectra: finer information on scaling and homogeneity
    • 45
    • Highly Influential
    • PDF
    Sharp weighted norm estimates beyond Calderón–Zygmund theory
    • 76
    • Highly Influential
    • PDF
    A restriction theorem for the Fourier transform
    • 112
    • PDF
    Endpoint estimates for the circular maximal function
    • 33
    • Highly Influential
    • PDF