TY - JOUR

T1 - Endpoint estimates for some maximal operators associated to the circular conical surface

AU - Heo, Yaryong R.

N1 - Funding Information:
This work was supported by the Korea Research Foundation Grant funded by the Korean Government KRF-2008-357-C00002. E-mail address: heo@math.wisc.edu.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2009/3/1

Y1 - 2009/3/1

N2 - For ψ ∈ C0∞ (Rd) and m > 0 we consider the maximal operator given byMm f (x, t) = under(sup, r > 0) | under(∫, Rd) f (x - y, t - | y |m) frac(1, rd) ψ (frac(y, r)) d y | . It is well known that Mm is a Lp-bounded operator for 1 < p ≤ ∞. Also A. Seeger and T. Tao proved that Mm is of weak-type L log log L if m ≠ 1. In this paper we consider the case m = 1 and prove M1 maps the standard Hardy space H1 to weak L1 if d ≥ 4.

AB - For ψ ∈ C0∞ (Rd) and m > 0 we consider the maximal operator given byMm f (x, t) = under(sup, r > 0) | under(∫, Rd) f (x - y, t - | y |m) frac(1, rd) ψ (frac(y, r)) d y | . It is well known that Mm is a Lp-bounded operator for 1 < p ≤ ∞. Also A. Seeger and T. Tao proved that Mm is of weak-type L log log L if m ≠ 1. In this paper we consider the case m = 1 and prove M1 maps the standard Hardy space H1 to weak L1 if d ≥ 4.

KW - Maximal functions

KW - Singular integrals

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U2 - 10.1016/j.jmaa.2008.10.011

DO - 10.1016/j.jmaa.2008.10.011

M3 - Article

AN - SCOPUS:56549114279

VL - 351

SP - 152

EP - 162

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -