On Entropy Bumps for Calderón-Zygmund Operators

Michael T. Lacey; Scott Spencer

Concrete Operators (2015)

  • Volume: 2, Issue: 1, page 47-52, electronic only
  • ISSN: 2299-3282

Abstract

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We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).

How to cite

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Michael T. Lacey, and Scott Spencer. "On Entropy Bumps for Calderón-Zygmund Operators." Concrete Operators 2.1 (2015): 47-52, electronic only. <http://eudml.org/doc/270883>.

@article{MichaelT2015,
abstract = {We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).},
author = {Michael T. Lacey, Scott Spencer},
journal = {Concrete Operators},
keywords = {weighted inequality; Ap; bumps; entropy; Calderón-Zygmund operators; entropy-bound method; weighted inequalities; -weights; maximal operator},
language = {eng},
number = {1},
pages = {47-52, electronic only},
title = {On Entropy Bumps for Calderón-Zygmund Operators},
url = {http://eudml.org/doc/270883},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Michael T. Lacey
AU - Scott Spencer
TI - On Entropy Bumps for Calderón-Zygmund Operators
JO - Concrete Operators
PY - 2015
VL - 2
IS - 1
SP - 47
EP - 52, electronic only
AB - We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).
LA - eng
KW - weighted inequality; Ap; bumps; entropy; Calderón-Zygmund operators; entropy-bound method; weighted inequalities; -weights; maximal operator
UR - http://eudml.org/doc/270883
ER -

References

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