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Displaying 121 – 140 of 227

On the Dirichlet and Neumann problems in multi-dimensional cone

Vladimir Vasilyev (2014)

Mathematica Bohemica

We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...

On the dual of weighted $H^{1} (| z | < 1)$

Richard Wheeden (1979)

Banach Center Publications

On the Evaluation of Certain Two-Dimensional Singular Integrals with Cauchy Kernels.

C. Dagnino, A. Palamara Orsi (1985)

Numerische Mathematik

On the Existence of Principal Values for the Cauchy Integral on Weighted Lebesgue Spaces for Non-Doubling Measures.

J. García-Cuerva, J.M. Martell (2001)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

On the existence of steady-state solutions to the Navier-Stokes system for large fluxes

Antonio Russo, Giulio Starita (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we deal with the stationary Navier-Stokes problem in a domain $Ω$ with compact Lipschitz boundary $\partial Ω$ and datum $a$ in Lebesgue spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of $\partial Ω$ , with possible countable exceptional set, provided $a$ is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for $Ω$ bounded.

On the expansion theorem described by $H (A, B)$ spaces.

El-Sabbagh, A.A. (2004)

International Journal of Mathematics and Mathematical Sciences

On the exponential integrability of fractional integrals on spaces of homogeneous type

A. Gatto, Stephen Vági (1993)

Colloquium Mathematicae

In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds $L^{1 / α}$ into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].

On the Fejér means of bounded Ciesielski systems

Ferenc Weisz (2001)

Studia Mathematica

We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space $H_{p}$ to $L_{p}$ if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n...

On the Fourier transform, Boehmians, and distributions

Dragu Atanasiu, Piotr Mikusiński (2007)

Colloquium Mathematicae

We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.

On the Fourier transform of the symmetric decreasing rearrangements

Philippe Jaming (2011)

Annales de l’institut Fourier

Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the $L^{2}$ behavior of a Fourier transform of a function over a small set is controlled by the $L^{2}$ behavior of the Fourier transform of its symmetric decreasing rearrangement. In the $L^{1}$ case, the same is true if we further assume that the function has a support of finite measure.As a byproduct, we also give...

On the Fourier-Laplace representation of analytic functions in tube domains.

I. Kh. Musin (1994)

Collectanea Mathematica

On the function of Marcinkiewicz

T. Walsh (1972)

Studia Mathematica

On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.

Jaak Peetre, Erik Svensson (1984)

Mathematica Scandinavica

On the global wellposedness of the 3-D Navier–Stokes equations with large initial data

Jean-Yves Chemin, Isabelle Gallagher (2006)

Annales scientifiques de l'École Normale Supérieure

On the $H^{p}$ - $L^{q}$ boundedness of some fractional integral operators

Pablo Rocha, Marta Urciuolo (2012)

Czechoslovak Mathematical Journal

Let $A_{1}, \dots, A_{m}$ be $n \times n$ real matrices such that for each $1 \leq i \leq m,$ $A_{i}$ is invertible and $A_{i} - A_{j}$ is invertible for $i \neq j$ . In this paper we study integral operators of the form $T f (x) = \int k_{1} (x - A_{1} y) k_{2} (x - A_{2} y) \dots k_{m} (x - A_{m} y) f (y) d y,$ $...$

On the Hermite expansions of functions from the Hardy class

Rahul Garg, Sundaram Thangavelu (2010) Studia Mathematica

Considering functions f on ℝⁿ for which both f and f̂ are bounded by the Gaussian

e^{- 1 / 2 a | x | ²}

, 0 < a < 1, we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)-finite functions, thus extending a one-dimensional result of Vemuri.

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