Harmonic sum and duality.
Harnachk Inequalities for Solutions of General Second Order Parabolic Equations and Estimates of Their Hölder Constants.
Harnack's Inequality for Elliptic Differential Equations on Minimal Surfaces.
Hausdorff measures of the set of critical values of functions of the class
Heat kernel estimates for critical fractional diffusion operators
We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.
Heisenberg uncertainty principles for some -analogue Fourier transforms.
Henstock-Kurzweil and McShane product integration; descriptive definitions
The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function is absolutely continuous. As a consequence we obtain that the McShane product integral of over exists and is invertible if and only if is Bochner integrable...
Henstock-Kurzweil integral on sets
The generalized Riemann integral of Pfeffer (1991) is defined on all bounded subsets of , but it is additive only with respect to pairs of disjoint sets whose closures intersect in a set of -finite Hausdorff measure of codimension one. Imposing a stronger regularity condition on partitions of sets, we define a Riemann-type integral which satisfies the usual additivity condition and extends the integral of Pfeffer. The new integral is lipeomorphism-invariant and closed with respect to the formation...
Henstock-Kurzweil type integrals in -adic harmonic analysis.
Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations
A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii spaces, for which every sheaf at a point can be amalgamated in a natural way. Let denote the space of continuous real-valued functions on with the topology of pointwise convergence. Our main result...
Herglotzův trik a rozklad kotangenty na parciální zlomky
Hermite and convexity.
Hermite-Hadamard inequality on time scales.
Hermite-Hadamard type inequalities for increasing radiant functions.
Hermite-Hadamard-type inequalities for generalized convex functions.
Hermite-Hadamard-type inequalities for increasing positively homogeneous functions.
Hessian determinants as elements of dual Sobolev spaces
In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.
Hidden lemmas in the early history of infinite series.
Hidden structures in the class of convex functions and a new duality transform
Our main intention in this paper is to demonstrate how some seemingly purely geometric notions can be presented and understood in an analytic language of inequalities and then, with this understanding, can be defined for classes of functions and reveal new and hidden structures in these classes. One main example which we discovered is a new duality transform for convex non-negative functions on attaining the value 0 at the origin (which we call “geometric convex functions”). This transform, together...
Higher integrability of determinants and weak convergence in L1.