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A representation of the sharp coefficient in a pointwise estimate for the gradient of the generalized Poisson integral of a function  f  onℝ  n{{\mathbb{R}}^{n}}    is obtained under the assumption that  f  belongs toL  p{L^{p}}   . The explicit value of the coefficient is found for the casesp  =  1{p=1}    andp  =  2{p=2}   .

Sharp estimates for the gradient of the generalized Poisson integral for a half-space