We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove th...We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.展开更多
文摘We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type （1, 1） inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension.
