Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version

Mathematics Subject Classification: 26D10.

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35

Hardy Inequality in Variable Exponent Lebesgue Spaces

Mathematics Subject Classification: 26D10, 46E30, 47B38

Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas

2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.

New Hardy-Type Inequalities with Singular Weights

2010 Mathematics Subject Classification: 26D10.

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75

Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces

MSC 2010: 26A33

Large Distinct Part Sizes in a Random Integer Partition

A partition of a positive integer n is a way of writing it as the sum of positive integers without regard to order; the summands are called parts. The number of partitions of n, usually denoted by p(n), is determined asymptotically by the famous partition formula of Hardy and Ramanujan [5]. We shall introduce the uniform probability measure P on the set of all partitions of n assuming that the probability 1/p(n) is assigned to each n-partition. The symbols E and V ar will be further used to denote the expectation and variance with respect to the measure P . Thus, each conceivable numerical characteristic of the parts in a partition can be regarded as a random variable.

A Note on Div-Curl Lemma

2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.