【摘 要】
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Let v =(v1,· · ·,vn)be a vector in Rn {0}.Consider the Laplacian on Rn with drift △v=∑ni=1((6)2/(6)x2i+2vi(6/(6)xi))and the measure d μ dμ(x)= e2dx,with
【出 处】
：
Harmonic Analysis and Applications(2014调和分析及其应用学术会议)
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Let v =(v1,· · ·,vn)be a vector in Rn {0}.Consider the Laplacian on Rn with drift △v=∑ni=1((6)2/(6)x2i+2vi(6/(6)xi))and the measure d μ dμ(x)= e2dx,with respect to which △v is self-adjoint.Let d and ▽ denote the Euclidean distance and the gradient operator on Rn.Consider the space(Rn,d,dμ),which has the property of exponential volume growth.We obtain weak type(1,1)for the Riesz transform ▽(-△v)-1/2 and for the heat maximal operator,with respect to dμ.Further,we prove that the uncentered Hardy-Littlewood maximal function is bounded on Lp for 1 ＜ p ≤ +∞ but not of weak type(1,1)if n ≥ 2.The uniform Lp(p ＞ 1)dimension independent bounds and surprising O(n)weak type(1,1)bound for the centered Hardy-Littlewood maximal function are obtained.
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