On equality in convolution inequalities

Towards characterizing equality in correlation inequalities

For most of the basic inequalities in mathematics we know conditions which completely specify the cases of equality. Many combinatorial correlation inequalities are special cases of the AD-inequality, as explained in [3, 8, 10]. However, for this inequality it seems to be difficult to classify the cases of equality. Certainly this is even more difficult for the much more general inequalities of...

Towards Characterising Equality in Correlation Inequalities

lVIULTIVARIATE PROBABILITY INEQUALITIES: CONVOLUTION THEORElVIS, COlVIPOSITION THEORElVlS, AND CONCENTRATION INEQUALITIES

Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form J!I (x )h(x (})dx, where usually !I = Ie is the indicator of a region C ~ R", h is a probability density on R , and (} is a translation parameter. Often fl and f2 possess convexity, monotonicity, and/or symmetry properties. More general multivariate compositions of the for...

Inequalities for Strongly Singular Convolution Operators

Best Constants for Two Non-convolution Inequalities

The norm of the operator which averages |f | in L p (R n) over balls of radius δ|x| centered at either 0 or x is obtained as a function of n, p and δ. Both inequalities proved are n-dimensional analogues of a classical inequality of Hardy in R 1. Finally, a lower bound for the operator norm of the Hardy-Littlewood maximal function on L p (R n) is given. A classical result of Hardy [HLP] states ...