We assume that X k = ∑ i = − ∞ + ∞ a i ξ i + k is a moving average process and { ξ i , − ∞ < i < + ∞ } is a doubly infinite sequence of identically distributed and dependent random variables with zero mean and finite variance and { a i , − ∞ < i < + ∞ } is an absolutely summable sequence of real numbers. Under suitable conditions of dependence, we get the precise rates in the law ...

Let T b → and T Π b be the commutators in the jth entry and iterated commutators of the multilinear Calderón-Zygmund operators, respectively. It was well known that the commutators of linear Calderón-Zygmund operators were not of weak type ( 1 , 1 ) and ( H 1 , L 1 ) , but they did satisfy certain endpoint L log L type estimates. In this paper, our aim is to give more natural sharp ...

By using the generalised Dirichlet integral inequality with continuous functions on the boundary of the upper half-space, we prove new types of solutions for the Neumann problem with fast-growing continuous data on the boundary. Given any harmonic function with its negative part satisfying similarly fast-growing conditions, we obtain weaker boundary integral condition.

The main purpose of this paper is to estimate the thickness of boundary layer for nonlinear evolution equations with damping and diffusion as the diffusion parameter β goes to zero. We prove that the thickness of layer is of the order O ( β γ ) with 0 < γ < 1 , thus improving the corresponding result in (Ruan and Zhu in Discrete Contin. Dyn. Syst. 32(1) 331-352, 2012 ) where 0 < γ ...

In the article, we discuss the monotonicity properties of the function x → ( 1 − e − a x p ) 1 / p / ∫ 0 x e − t p d t for a , p > 0 with p ≠ 1 on ( 0 , ∞ ) and prove that the double inequality Γ ( 1 + 1 / p ) ( 1 − e − a x p ) 1 / p < ∫ 0 x e − t p d t < Γ ( 1 + 1 / p ) ( 1 − e − b x p ) 1 / p holds for all x > 0 if and only if a ≤ min { 1 , Γ − p ( 1 + 1 / p ) } and b ≥ max { 1 , ...

In the present paper, we shall give a characterization for the Spanne and Adams type boundedness of the Riesz potential and its commutators on the generalized Orlicz-Morrey spaces, respectively. Also we give criteria for the weak versions of Spanne and Adams type boundedness of the Riesz potential on the generalized Orlicz-Morrey spaces. In all the cases the conditions for the ...

By applying some Schrödinger-type inequalities developed by Huang (Int. J. Math. 27(2):1650009, 2016 ), we are concerned with stabilization of discrete linear systems associated with the Schrödinger operator. Our first aim is to prove a state-dependent switching law associated with the Schrödinger operator, which is based on a convex combination. Next, we derive sufficient ...

The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by e i t Δ α , 0 < α < 1 . Combining the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalities. MSC: 22E25, 33C45, 35H20, 35B40.

Probabilistic frames have some properties which are similar to those of frames in Hilbert space. Some equalities and inequalities have been established for traditional frames. In this paper, we give some equalities and inequalities for probabilistic frames. Our results generalize and improve the remarkable results which have been obtained.

Bernstein inequality is an essential inequality for Besov spaces. Smoothness based approaches are widely used in establishing the inequality. Yet, despite numerous studies over the last two decades, there is still little research focusing on decay-based approaches. However, motivating authors to establish inequality poses challenges, many of which can be overcome by means of the ...

Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k : k ∈ Z } , where A is a real n × n matrix with all its eigenvalues λ satisfy | λ | > 1 . Let φ ...

We prove and discuss some new H p - L p type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed ...

In this paper, we construct the geometric inequalities for the squared norm of the mean curvature and warping functions of warped product semi-slant submanifolds in Kenmotsu space forms. The equality cases are also discussed. MSC: 53C40, 58C35, 53C55, 53C42, 53C15, 53D15.

In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided. To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system. We examine our results ...

This paper deals with the existence and multiplicity of symmetric solutions for a weighted semilinear elliptic system with multiple critical Hardy-Sobolev exponents and singular potentials in R N . Applying the symmetric criticality principle and Caffarelli-Kohn-Nirenberg inequality, we establish several existence and multiplicity results of G-symmetric solutions under certain ...

The complete characterization of the weighted L p − L r inequalities of supremum operators on the cones of monotone functions for all 0 < p , r ≤ ∞ is given. MSC: 26D15, 47G10.

This paper shows some continuities of mappings between the space of mixed variational inequality problems and the graph space of their solution mappings. The space of mixed variational inequality problems is homeomorphic to the graph of a continuous mapping. These generalize the results in the corresponding references. MSC: 49J53, 58E35, 47H04.

We aim to present some new Pólya-Szegö type inequalities associated with Hadamard k-fractional integral operators, which are also used to derive some Chebyshev type integral inequalities. Further we apply some of the results presented here to a function which is bounded by the Heaviside functions. MSC: 26A33, 26D10, 26D15.

This paper investigates the boundary behaviors for linear systems of subsolutions of the stationary Schrödinger equation, which contain unstable subsystems. Our first aim is to establish a state-feedback switching law guaranteeing the continuous-time systems to be uniformly exponentially stable. And then we present sufficient and necessary for the stability of the systems with two ...

In this paper, a modified feasible semi-smooth asymptotically Newton method for nonlinear complementarity problems is proposed. The global convergence of the method and superlinear convergence are proved under some suitable assumptions. Numerical experiments are included to highlight the efficacy of the modified algorithm. MSC: 90C33.

This paper considers the following semilinear pseudo-parabolic equation with a nonlocal source: u t − △ u t − △ u = u p ( x , t ) ∫ Ω k ( x , y ) u p + 1 ( y , t ) d y , and it explores the characters of blow-up time for solutions, obtaining a lower bound as well as an upper bound for the blow-up time under different conditions, respectively. Also, we investigate a nonblow-up ...

Zero point problems of two accretive operators and fixed point problems of a nonexpansive mappings are investigated based on a Mann-like iterative algorithm. Weak convergence theorems are established in a Banach space. MSC: 47H06, 47H09, 90C33.

In this paper, we first study the deterministic Swift-Hohenberg equation on a bounded domain. After obtaining some a priori estimates by the uniform Gronwall inequality, we prove the existence of an attractor by the Sobolev compact embeddings. Then, we consider the stochastic Swift-Hohenberg equation driven by additive noise on an unbounded domain and prove that the random ...

In this paper, we introduce the L p -mixed mean zonoid of convex bodies K and L, and we prove some important properties for the L p -mixed mean zonoid, such as monotonicity, GL ( n ) covariance, and so on. We also establish new affine isoperimetric inequalities for the L p -mixed mean zonoid. MSC: 52A30, 52A40.

By decomposing functions, we establish some boundedness results for some rough singular integrals on the homogeneous Morrey-Herz spaces M K ˙ q , p ( ⋅ ) α ( ⋅ ) , λ ( R n ) , where the two main indices are variable. The corresponding results as regards their commutators are also considered. MSC: 42B20, 42B25.