L p weighted inequalities for the dyadic square function

Akihito Uchiyama

Studia Mathematica (1995)

  • Volume: 115, Issue: 2, page 135-149
  • ISSN: 0039-3223

Abstract

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We prove that ʃ ( S d f ) p V d x ≤ C p , n ʃ | f | p M d ( [ p / 2 ] + 2 ) V d x , where S d is the dyadic square function, M d ( k ) is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.

How to cite

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Uchiyama, Akihito. "$L^p$ weighted inequalities for the dyadic square function." Studia Mathematica 115.2 (1995): 135-149. <http://eudml.org/doc/216204>.

@article{Uchiyama1995,
abstract = {We prove that $ʃ(S_df)^pVdx ≤ C_\{p,n\}ʃ |f|^p M_d^\{([p/2]+2)\}Vdx$, where $S_d$ is the dyadic square function, $M_d^\{(k)\}$ is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.},
author = {Uchiyama, Akihito},
journal = {Studia Mathematica},
keywords = {dyadic square function; dyadic maximal function; weighted inequality; BMO},
language = {eng},
number = {2},
pages = {135-149},
title = {$L^p$ weighted inequalities for the dyadic square function},
url = {http://eudml.org/doc/216204},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Uchiyama, Akihito
TI - $L^p$ weighted inequalities for the dyadic square function
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 2
SP - 135
EP - 149
AB - We prove that $ʃ(S_df)^pVdx ≤ C_{p,n}ʃ |f|^p M_d^{([p/2]+2)}Vdx$, where $S_d$ is the dyadic square function, $M_d^{(k)}$ is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.
LA - eng
KW - dyadic square function; dyadic maximal function; weighted inequality; BMO
UR - http://eudml.org/doc/216204
ER -

References

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  10. [W1] J. M. Wilson, Weighted inequalities for the dyadic square functions without dyadic A ∞ , Duke Math. J. 55 (1987), 19-49. 
  11. [W2] J. M. Wilson, A sharp inequality for the square function, ibid., 879-887. Zbl0639.42017
  12. [W3] J. M. Wilson, L p weighted norm inequalities for the square function 0< p< 2, Illinois J. Math. 33 (1989), 361-366. 
  13. [W4] J. M. Wilson, Weighted inequalities for the square function, in: Contemp. Math. 91, Amer. Math. Soc., 1989, 299-305. 
  14. [W5] J. M. Wilson, Weighted norm inequalities for the continuous square function, Trans. Amer. Math. Soc. 314 (1989), 661-692. Zbl0689.42016
  15. [W6] J. M. Wilson, Chanillo-Wheeden inequalities for 0< p≤ 1, J. London Math. Soc. (2) 41 (1990), 283-294. Zbl0712.42032
  16. [W7] J. M. Wilson, Some two-parameter square function inequalities, Indiana Univ. Math. J. 40 (1991), 419-442. Zbl0734.42007

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