The pointillist principle for variation operators and jump functions

• Kevin Hughes ^[1]
  1. [1] Edinburgh Napier University

     Edinburgh Napier University

     Reino Unido

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 2, 2025, págs. 577-588
• Idioma: inglés
• DOI: 10.33044/revuma.4124
• Enlaces
  • Texto completo
• Resumen

  • I extend the pointillist principles of Moon and Carrillo–de Guzmán to variational operators and jump functions.

• Referencias bibliográficas
  • J. Bourgain, Pointwise ergodic theorems for arithmetic sets, Inst. Hautes Etudes Sci. Publ. ´ Math. no. 69 (1989), 5–45, with an appendix...
  • M. Carena, Weak type (1, 1) of maximal operators on metric measure spaces, Rev. Un. Mat. Argentina 50 no. 1 (2009), 145–159. MR Zbl
  • H. Carlsson, A new proof of the Hardy–Littlewood maximal theorem, Bull. London Math. Soc. 16 no. 6 (1984), 595–596. DOI MR Zbl
  • M. T. Carrillo and M. de Guzman´ , Maximal convolution operators and approximations, in Functional analysis, holomorphy and approximation...
  • L. Grafakos and M. Masty lo, Restricted weak type versus weak type, Proc. Amer. Math. Soc. 133 no. 4 (2005), 1075–1081. DOI MR Zbl
  • R. L. Jones, A. Seeger, and J. Wright, Strong variational and jump inequalities in harmonic analysis, Trans. Amer. Math. Soc. 360 no. 12 (2008),...
  • D. Kosz, On the discretization technique for the Hardy–Littlewood maximal operators, Real Anal. Exchange 41 no. 2 (2016), 287–292. MR Zbl...
  • A. D. Melas, The best constant for the centered Hardy–Littlewood maximal inequality, Ann. of Math. (2) 157 no. 2 (2003), 647–688. DOI MR Zbl
  • M. T. Menarguez and F. Soria, Weak type (1, 1) inequalities of maximal convolution operators, Rend. Circ. Mat. Palermo (2) 41 no. 3 (1992),...
  • M. Mirek, E. M. Stein, and B. Trojan, ℓ p(Z d)-estimates for discrete operators of Radon type: variational estimates, Invent. Math. 209 no....
  • K. H. Moon, On restricted weak type (1, 1), Proc. Amer. Math. Soc. 42 (1974), 148–152. DOI MR Zbl
  • G. Pisier and Q. H. Xu, The strong p-variation of martingales and orthogonal series, Probab. Theory Related Fields 77 no. 4 (1988), 497–514....
  • A. Seeger, T. Tao, and J. Wright, Pointwise convergence of lacunary spherical means, in Harmonic analysis at Mount Holyoke (South Hadley,...
  • A. Seeger and J. Wright, Problems on averages and lacunary maximal functions, in Marcinkiewicz centenary volume, Banach Center Publ. 95, Polish...