Ein system von funktionalgleichungen vom Verallgemeinerten Replikativitäts-Typ

Ohne Zusammenfassung

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Idempotents of Fourier multiplier algebra

We prove that if the indicator-function1 _E of a measurable setE is a Fourier multiplier in the spaceE ^p () for somep2 thenE is an open set (up to a set of measure zero).     

Ideal weights: Asymptotically optimal versions of doubling, absolute continuity, and bounded mean oscillation

Sharp inequalities between weight bounds (from the doubling, A_p, and reverse Hölder conditions) and the BMO norm are obtained when the former are near their optimal values. In particular, the BMO norm of the logarithm of a weight is controlled by the square root of the logarithm of its A_∞ bound. These estimates lead to a systematic development of asymptotically sharp higher integrability results for reverse Hölder weights and extend Coifman and Fefferman's formulation of the A_∞ condition as an equivalence relation on doubling measures to the setting in which all bounds become optimal over small scales.     

Ordinary and strong density continuity of complex analytic functions

In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:²²,G(x,y)=(x,y ³ ), is not density continuous [1]. We will also characterize those analytic functions which are strongly density continuous at the given pointa . From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b andb is either real or imaginary.     

Cylinder Multipliers Associated with a Convex Polygon

In this paper we prove that sharp weak-type estimates for the maximal operators associated with a cylindric distance function associated with a convex polygon on when 2/3 < p < 1 and , or when p = 2/3 and . This work was supported (in part) by research funds from Chosun University, 2007.     

Ona-Wright convexity and the converse of Minkowski's inequality

Summary Leta (0, 1/2] be fixed. A functionf satisfying the inequalityf(ax + (1 – a)y) + f((1 – a)x + ay) f(x) + f(y), called herea-Wright convexity, appears in connection with the converse of Minkowski's inequality. We prove that every lower semicontinuousa-Wright convex function is Jensen convex and we pose an open problem. Moreover, using the fact that 1/2-Wright convexity coincides with Jensen convexity, we prove a converse of Minkowski's inequality without any regularity conditions.     

On Darboux solutions of the Euler's equation

Summary We construct a non-constant Darboux functionf: R R which is a solution of the Euler's functional equationf(x + f(x)) = f(x) for everyx. This function is a counter-example to a statement given in the literature.     

Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. II

This paper continues the investigation of weight problems in Orlicz classes for maximal functions and singular integrals defined on homogeneous type spaces considered in [1].     

Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces

The necessary and sufficient conditions are derived in order that a strong type weighted inequality be fulfilled in Orlicz classes for scalar and vector-valued maximal functions defined on homogeneous type spaces. A weak type problem with weights is solved for vector-valued maximal functions.     

On two mean value properties and functional equations associated with them

Summary Motivated by different mean value properties, the functional equationsf(x) – f(y)/x–y=[(x, y)], (i)xf(y) – yf(x)/x–y=[(x, y)] (ii) (x y) are completely solved when, are arithmetic, geometric or harmonic means andx, y elements of proper real intervals. In view of a duality between (i) and (ii), three of the results are consequences of other three.The equation (ii) is also solved when is a (strictly monotonic) quasiarithmetic mean while the real interval contains 0 and when is the arithmetic mean while the domain is a field of characteristic different from 2 and 3. (A result similar to the latter has been proved previously for (i).)     

Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I

Criteria of various weak and strong type weighted inequalities are established for singular integrals and maximal functions defined on homogeneous type spaces in the Orlicz classes.     

On discrete and continuous norms in Paley-Wiener spaces and consequences for exponential frames

It is well known that for certain sequences {t_n}_n the usual L^p norm ·_p in the Paley-Wiener space PW ^p is equivalent to the discrete norm f_p,{tn}:=( _n=– |f(t_n)|^p)^1/p for 1 p = < and f_,{tn}:=sup _n|f(t_n| for p=). We estimate f_p from above by Cf_p, _n and give an explicit value for C depending only on p, , and characteristic parameters of the sequence {t_n}_n. This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer.     

Equations fonctionnelles et recherche de sous-groupes

Sans résumé

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Dedié à János Aczél à l'occasion de son 60ème anniversaire     

Almost everywhere convergence of Ciesielski-Fourier series of <Emphasis Type="Italic">H</Emphasis><Subscript>1</Subscript>functions

It is proved that a lacunary sequence of the Ciesielski-Fourier series of converges almost everywhere to f. Received: 8 September 2003