Hardy spaces on compact Lie groups
Hardy spaces on SU(2)
Hardy Spaces on the Plane and Double Fourier Transforms.
Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients
Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) (1/2 < p≤2) where f belongs to the Hardy space defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.
Hardy-Littlewood type inequalities for Laguerre series.
Hardy's inequality for compact Lie groups.
Hardy's integral inequality for commutators of Hardy operators.
Hardy-type inequalities for Hermite expansions.
Hardy-type inequalities on the real line.
Harmonic Analysis and nonstandard Brownian Motion in the plane.
Harmonic analysis and the geometry of subsets of Rn.
This subject has several natural points of view, but we shall start with the one that corresponds to the following question: Is there something like Littlewood-Paley theory which is useful for analyzing the geometry of subsets of Rn, in much the same way that traditional Littlewood-Paley theory is good for analyzing functions and operators?
Harmonic analysis of the space BV.
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is almost characterized by wavelet expansions in the following sense: if a function f is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-l1 type estimates. These weak estimates can be employed to prove many interesting results. We use them to identify the interpolation spaces between BV and Sobolev...
Harmonic analysis on the group of rigid motions of the Euclidean plane
Harmonic functions and Hardy spaces on trees with boundaries
Hausdorff and Fourier dimension
There is no constraint on the relation between the Fourier and Hausdorff dimension of a set beyond the condition that the Fourier dimension must not exceed the Hausdorff dimension.
Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica
ACM Computing Classification System (1998): G.1.2.Moduli for numerical finding of the polynomial of the best Hausdorff approximation of the functions which differs from zero at just one point or having one jump and partially constant in programming environment MATHEMATICA are proposed. They are tested for practically important functions and the results are graphically illustrated. These moduli can be used for scientific research as well in teaching process of Approximation theory and its application....
Hausdorff dimension of the graph of the fractional Brownian sheet.
Hausdorff dimension, projections, and the Fourier transform.
This is a survey on transformation of fractal type sets and measures under orthogonal projections and more general mappings.
Hausdorff operator on Morrey spaces and Campanato spaces
We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).
Heat-diffusion and Poisson integrals for Laguerre and special Hermite expansions on weighted spaces
We investigate heat-diffusion and Poisson integrals associated with Laguerre and special Hermite expansions on weighted spaces with weights.