Inequalities with Weights for Discrete Hilbert Transforms✝

New half-discrete Hilbert inequalities for three variables

In this paper, we obtain two new half-discrete Hilbert inequalities for three variables. The obtained inequalities are with the best constant factor. Moreover, we give their equivalent forms.

DISCRETE RIESZ TRANSFORMS AND SHARP METRIC Xp INEQUALITIES

For p ∈ [2,∞) the metric Xp inequality with sharp scaling parameter is proven here to hold true in Lp. The geometric consequences of this result include the following sharp statements about embeddings of Lq into Lp when 2 < q < p <∞: the maximal θ ∈ (0, 1] for which Lq admits a bi-θ-Hölder embedding into Lp equals q/p, and for m,n ∈ N the smallest possible bi-Lipschitz distortion of any embeddi...

On More Accurate Reverse Multidimensional Half–discrete Hilbert–type Inequalities

By using the methods of weight functions and Hermite-Hadamard’s inequality, two kinds of more accurate equivalent reverse multidimensional half-discrete Hilbert-type inequalities with the kernel of hyperbolic cotangent function are given. The constant factor related to the Riemann zeta function is proved to be the best possible. Mathematics subject classification (2010): 26D15, 47A07, 37A10.

Two-dimensional Hilbert Transforms'

Weighted Norm Inequalities for Hilbert Transforms and Conjugate Functions of Even and Odd Functions1

It is well known that the Hilbert tranformation and the conjugate function operator restricted to even (odd) functions define bounded linear operators on weighted If spaces under more general conditions than is the case for the unrestricted operators. In analogy with recent results of Hunt, Muckenhoupt and Wheeden for the Hilbert transform and the conjugate function operator, we obtain necessar...