Volume 19, Issue 3

Abstract. Let be a bounded oriented connected open subset of whose boundary is a compact topological surface . We consider non-standard generalized Hölder spaces, denoted by , of Clifford algebra-valued functions u , whose local modulus of continuity in the variable t for each has a majorant , which may vary from point to point. The main purpose of this paper is to prove the boundedness of the Clifford singular integral operator in the spaces , when is an Ahlfors–David regular surface of ℝ n . This can be viewed as the Plemelj–Privalov theorem on generalized Hölder spaces in the variable exponent Clifford analysis setting.

Abstract. In this paper we prove the almost everywhere convergence of a special subsequence of the logarithmic means of integrable functions, for every , where and I is the group of 2-adic integers. We suppose that It proves that a.e. as for every , too.

Abstract. In this article we present the classical theory of Chebyshev polynomials starting from the definition of a family of complex polynomials, including both the first and second kind classical Chebyshev polynomials, which are related to their real and imaginary parts. This point of view permits one to derive a lot of generating functions and relations between Chebyshev families of two kinds, which are essentially new, as exponential generating functions, bilinear and bilinear exponential generating functions. We also deduce relevant relations for products of Chebyshev polynomials and the related generating functions.

Abstract. Let R be a prime ring with its Utumi ring of quotients U , the extended centroid of R , H a generalized derivation of R and L a noncentral Lie ideal of R . Suppose that there exists such that for all , where is a fixed integer. Then one of the following holds: (i) There exists such that for all , unless R satisfies s 4 . (ii) , R satisfies s 4 and there exists an element such that for all . (iii) and R satisfies s 4 .

Abstract. Bitopological spaces in which every subset is -open in its -closure (i.e., ( i , j )-submaximal spaces) are introduced and their properties are studied. Based on the investigations by Arhangel'skiĭ, Collins and the author, the necessary conditions are found for bitopological spaces to be p -connected. Furthermore, ( i , j )- I -spaces are introduced and the relations between ( i , j )-submaximal, ( i , j )-nodec and ( i , j )- I -spaces are established when two topologies on a set are either independent of each other or interconnected by the inclusion, -, - and -relations. The preservation of ( i , j )-submaximal and ( 2 , 1 )- I -spaces under morphisms is also considered.

Abstract. We classify all indecomposable P-torsion modules over a pullback of two Dedekind domains. The results given in [Czechoslovak Math. J. 59 (2009), 1103–1114] are extended to a more general P-torsion modules case.

Abstract. The Wiener–Hopf factorization of trigonometric polynomial matrix functions is considered and it is proved that the factors are matrices of trigonometric polynomials as well. The natural bounds for partial indices and for orders of the factors are obtained.

Abstract. The paper introduces a new concept of Λ-variation of bivariate functions and investigates its connection with the convergence of double Fourier series.

Abstract. We study the semigroup of monotone injective partial selfmaps of the set of integers having cofinite domain and image. We show that is bisimple and all of its non-trivial semigroup homomorphisms are either isomorphisms or group homomorphisms. We also prove that every Baire topology on , such that is a Hausdorff semitopological semigroup, is discrete and we construct a non-discrete Hausdorff inverse semigroup topology on . We show that the discrete semigroup cannot be embedded into some classes of compact-like topological semigroups and that its remainder under the closure in a topological semigroup S is an ideal in S .

Abstract. A characterization of the boundedness for multiple kernel operators defined with respect to a product Borel measure on is established. Necessary and sufficient conditions are formulated for the two-weighted (two-measured) inequalities for the multiple Hardy and Riemann–Liouville transforms defined by product measures. A similar result for the strong one-sided fractional maximal operator is also derived. In all cases the target Lebesgue spaces are defined by a measure having, generally speaking, non-product form. As a corollary we have, for example, two-weighted criteria for discrete multiple Hardy transforms. A Fefferman–Stein type inequality for the multiple Riemann–Liouville transform defined with respect to a measure is derived in the diagonal case.

Abstract. In this paper, we introduce a new class of generalized Hermite–Bernoulli polynomials and derive some implicit summation formulae and symmetric identities by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli polynomials studied by Pierpaolo Natalini and Angela Bernardini, Bernoulli numbers, Bernoulli polynomials and Hermite polynomials.

Abstract. In this work, we find conditions on data guaranteeing the global nonexistence of solutions to inverse source problems for a class of Petrovsky systems. We also establish asymptotic stability results for the corresponding problems with the opposite sign of power-type nonlinearities and the integral constraint vanishing as time tends to infinity.

Abstract. This is a comment on the papers from Elkies [Amer. Math. Monthly 110 (2003), 561–573] and Cvijović–Klinowski [J. Comput. Appl. Math. 142 (2002), 435–439]. We provide an explicit expression for the kernel of the integral operator introduced in Elkies' paper. This explicit expression considerably simplifies the calculation of and enables a simple derivation of Cvijović and Klinowski's integral representation for .