Analysis Mathematica最新文献

In this paper, we introduce the weighted anisotropic local Hardy spaces (h_{w, N}^p(mathbb{R}^n ; A)) with (pin(0,1] ), via the local non-tangential grand maximal function. We alsoestablish the atomic decompositions for the weighted anisotropic local Hardy spaces (h_{w, N}^p(mathbb{R}^n ; A)). In addition, we obtain the duality between (h_{w, N}^p(mathbb{R}^n ; A)) and the weighted anisotropic Campanato type spaces.

We establish a criteria for the propagation of algebraic dependence of a set of differentiably non-degenerate meromorphic mappings from a complete and stochastically complete Kähler manifold M into a complex projective manifold, based on certain diffusion method. As its applications, we also consider the unicity problems for differentiably non-degenerate meromorphic mappings of M into a complex projective space in Nevanlinna theory.

This paper explores the boundedness of Fourier multipliers from (L_p) to (L_q). We present new results that improve upon classical theorems due to Hörmander, Lizorkin, and Marcinkiewicz. In addition, we provide necessary conditions for the boundedness of Fourier multipliers. We introduce the concept of (M)-generalized monotone functions and sequences and derive criteria for the boundedness of Fourier multipliers corresponding to them.

We prove some new results and unify old ones on the complete monotonicity of functions including the gamma and digamma functions and their q-analogues. All of these results lead to new and interesting inequalities. Of particular interest, we obtain the following results:for all (q>0), (qneq 1), (x>0) and (nin mathbb{N}), we have

where (P_n(x)) is some polynomial of degree n to be defined later.

These inequalities are the q-analogues of the classical inequalities

and

In the present paper Riesz sums of Fourier-Chebyshev rational integral operators with restrictions on the number of geometrically distinct poles are introduced. Approximation of the function ((1-x)^gamma), (gamma in (0,1)), by this method is considered. Estimates of pointwise and uniform approximation are established,as well as asymptotic expressions for the uniform approximation majorant. Additionally, the optimal values of the parameters of the approximating function, at which the rate of decrease of the majorant is the greatest are found. In the case of Riesz sums of a polynomial Fourier-Chebyshev series, approximation of functions satisfying the Lipschitz condition of order (gamma) on the segment ([-1,1]) is investigated.

Sufficient conditions for the uniform boundedness of the Steklov averaging operators in weighted variable exponent spaces of periodic functions are obtained.The boundedness of the Steklov averages was previously known if the exponent satisfies the Dini-Lipschitz condition and a local analogue of the Muckenhoupt condition holds. In this paper, the boundedness of the Steklov averages is established under certain Muckenhoupt type conditions solely, and the Dini-Lipschitz condition is not required. The norms of averaging operators are estimated explicitly.

In this article we present the definition of the generalized maximal operator (M_Phi) acting on measures and we prove some of its basic properties. More precisely, we demonstrate that (M_Phi) satisfies a Kolmogorov inequality and that this operator is of weak type ((1,1)). This allow us to obtain a family of (A_p) weights involving the distance (d(x,F)) to a closed set (F) in a framework of Ahlfors spaces. Also, we prove that (M_Phi) satisfies a weighted modular weak type inequality associated to the Young function (Phi), and we give another one that yields a sufficient condition for the weight to belong to the (A_1) class.

In this work we deal with a singular evolution equation of the form

where both (A) and (E) are linear operators, with (E) bounded but not necessarily injective, defined in adequate subspaces of a given Banach space (X). By using the concept of generalized semigroups, our goal is to prove a Hille-Yosida type theorem for this problem, that is, to find necessary and sufficient conditions under which (A) is the generator of a generalized semigroup ({U(t) : t geq 0}). This problem is dealt with by making use of the (E)-spectral theory and the concept of generalized integrable families. Finally, we present an abstract example that illustrates the theory.

We characterize the geometrically doubling condition of a metric space in terms of the uniform (L^1)-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.

In the general setting of a locally compact Abelian group G, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions (f colon G to mathbb{R}) satisfying (f(0) = 1) and having (supp f_{+} subset Omega) for some measurable subset (Omega) of finite measure. In this paper, we consider the question of the existence of an extremal function for the Delsarte extremal problem. In particular, we show that there exists an extremal function for the Delsarte problem when (Omega) is closed, extending previously known existence results to a larger class of functions.