Transmission of convergence

Neugebauer, Christoph J.

  • Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 193-215

Abstract

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If E ( f ) = { x : lim sup f ☆ μ j ( x ) > lim inf f ☆ μ j ( x ) } , we examine the type of convergence of g k to f so that | E ( g k ) | ≤ M , k = 1 , 2 , ⋯ , implies | E ( f ) | ≤ M .

How to cite

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Neugebauer, Christoph J.. "Transmission of convergence." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 2003. 193-215. <http://eudml.org/doc/220957>.

@inProceedings{Neugebauer2003,
abstract = {If $E(f)=\lbrace x:\limsup f\star \mu _j(x)>\liminf f\star \mu _j(x)\rbrace $, we examine the type of convergence of $g_k$ to $f$ so that $|E(g_k)|\le M$, $k=1,2,\dots $, implies $|E(f)|\le M$.},
author = {Neugebauer, Christoph J.},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {measure; convergence; maximal operator; minimal operator},
location = {Praha},
pages = {193-215},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {Transmission of convergence},
url = {http://eudml.org/doc/220957},
year = {2003},
}

TY - CLSWK
AU - Neugebauer, Christoph J.
TI - Transmission of convergence
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 2003
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 193
EP - 215
AB - If $E(f)=\lbrace x:\limsup f\star \mu _j(x)>\liminf f\star \mu _j(x)\rbrace $, we examine the type of convergence of $g_k$ to $f$ so that $|E(g_k)|\le M$, $k=1,2,\dots $, implies $|E(f)|\le M$.
KW - measure; convergence; maximal operator; minimal operator
UR - http://eudml.org/doc/220957
ER -

References

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  1. Uribe D. Cruz,- Neugebauer C. J., Weighted norm inequalities for the geometric maximal operator, Publ. Mat. 42 (1998), 239–263. Zbl 0919.42014, MR 99e:42029. (1998) MR1628101
  2. Uribe D. Cruz,- SFO,, Neugebauer C. J., Olesen V., Norm inequalities for the minimal and maximal operator, and differentiation of the integral, Publ. Mat. 41 (1997), 577–604. Zbl 0903.42007, MR 99b:42022. (1997) MR1485505
  3. Uribe D. Cruz,- SFO,, Neugebauer C. J., Olesen V., Weighted norm inequalities for a family of one-sided minimal operators, Illinois J. Math. 41 (1997), 77–92. Zbl 0871.42019, MR 99b:42021. (1997) MR1433187
  4. Cuerva J. García,- Francia J. L. Rubio de, Weighted norm inequalities and related topics, North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985. Zbl 0578.46046, MR 87d:42023. (1985) MR0807149
  5. Muckenhoupt B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. Zbl 0236.26016, MR 45 #2461. (1972) Zbl0236.26016MR0293384
  6. Stein E. M., Harmonic analysis: real variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series 43. Princeton University Press, Princeton, N. J., 1993. Zbl 0821.42001, MR 95c:42002. (1993) Zbl0821.42001MR1232192

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