Related papers: A sharp interpolation between the H\"older and Gau…
The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases for finite groups and finite dimensional Kac algebras. We…
The generalized Young inequality on the Lorentz spaces for commutative hypergroups is introdused and an application of it is given to the theory of fractional integrals. The boundedness on the Lorentz space and the Hardy-Littlewood-Sobolev…
We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in [Hairer-Xu], but with…
We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of…
In this paper, we have derived certain classical inequalities, namely, Young's, H\"older's, Minkowski's and Hermite-Hadamard inequalities for pseudo-integral (also known as $g$-integral). For Young's, H\"older's, Minkowski's inequalities,…
We study interpolation properties of operators (not necessarily linear) which satisfy a specific $K$-inequality corresponding to endpoints defined in terms of Orlicz--Karamata spaces modeled upon the example of the Gaussian--Sobolev…
Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms…
In this paper, we highlight a new computational aspect of Nonstandard Analysis relating to higher-order computability theory. In particular, we prove that the Gandy-Hyland functional equals a primitive recursive functional involving…
We prove a new type of Poincar\'e inequality on abstract Wiener spaces for a family of probability measures which are absolutely continuous with respect to the reference Gaussian measure. This class of probability measures is characterized…
In the case of a compact orientable pseudomanifold, a well-known theorem of M. Goresky and R. MacPherson says that the cap product with a fundamental class factorizes through the intersection homology groups. In this work, we show that this…
We study fully-discrete approximations and quadratures of infinite-variate functions in abstract Bochner spaces associated with a Hilbert space $X$ and an infinite-tensor-product Jacobi measure. For target infinite-variate functions taking…
We give H\"older's inequalities for integral and conditional expectation involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for the operator are established.
The classical hypercontractive inequality for the noise operator on the discrete cube plays a crucial role in many of the fundamental results in the Analysis of Boolean functions, such as the KKL (Kahn-Kalai-Linial) theorem, Friedgut's…
We present a new approach to the Marcinkiewicz interpolation inequality for the distribution function of the Hilbert transform, and prove an "abstract" version of this inequality. The approach uses "logarithmic determinants" and new…
Higher order terms in the effective action of noncommutative gauge theories exhibit generalizations of the *-product (e.g. *' and *-3). These terms do not manifestly respect the noncommutative gauge invariance of the tree level action. In…
We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some…
The theory of Wilson loops for gauge theories with unitary gauge groups is formulated in the language of symmetric functions. The main objects in this theory are two generating functions, which are related to each other by the involution…
We generalize Abrahamse's interpolation theorem from the setting of a multiply connected domain to that of a more general Riemann surface. Our main result provides the scalar-valued interpolation theorem for the fixed-point subalgebra of…
We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and…