Fejér's theorem for the classesV p

La successione di elementi di una serie di Fourier derivata di una funzione appartenente alla classe di WienerV _p,p>1 (rispettivamente alla classe di Waterman {n ^β}B V o à quella di ChanturiyaV [n ^β] per qualsiasi 0<β<1) è sommabile verso (f(x+0)?f(x?0))/π mediante i metodi di Cèsaro di ordine α>1?1/p (α>β).     

Estimates of the levy constant for\sqrt p and class number one criterion for ℚ(\sqrt p )

Let p ≡ = 3 (mod 4) be a prime, let ?( $\sqrt p $ ) be the length of the period of the expansion of $\sqrt p $ into a continued fraction, and let h(4p) be the class number of the field ?( $\sqrt p $ ). Our main result is as follows. For p > 91, h(4p)=1 if and only if ?( $\sqrt p $ ) > 0.56 $\sqrt p $ L_4p(1), where L_4p(1) is the corresponding Dirichlet series. The proof is based on studying linear relations between convergents of the expansion of $\sqrt p $ into a continued fraction. Bibliography: 13 titles.     

L p -Estimates for the Navier–Stokes Equations for Steady Compressible Flow

We consider the Navier–Stokes equations for compressible isentropic flow in the steady three-dimensional case. The pressure and the kinetic energy are estimated uniformly in L^q with being the density. This is an improvement of known estimates in the case Mathematics Subject Classification (2000): 35Q30, 76N10     

Parameter Estimation for the NEAR（p） Model

As to the acronym NEAR(p), it means "New Exponential Autoregressive Process of order p". The NEAR(p) model is denned by where α0,α1,α2… are non-negative and sum to unity, and the residual sequence{εt} is defined as where q1, q2, … , qp+1 are non-negative and sum to unity, and {Et} is an independent and identically distributed (i.i.d.) sequence of standard exponential variants. Chan showed necessary and sufficient conditions for the existence of a stationary and ergodic NEAR(p) model.     

Empirical Likelihood Inference for AR（p） Model

In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared.     

Positive Solutions for Semipositone ( p,n − p ) Right Focal Boundary Value Problems

We consider the ( p , n m p ) right focal boundary value problem: $${\matrix{{(- 1)^{n - p} u^{(n)} \! = \lambda \;f(t, u), } \hfill & \ {{\rm for }\ 0 \lt t \lt 1, } \hfill \cr \quad \quad \,{u^{(i)} (0) = 0, } \hfill & {0 \le i \le p - 1, } \hfill \cr \quad \quad \,{u^{(i)} (1) = 0, } \hfill & {p \le i \le n - 1, } \hfill \cr}} $$ where 1 h p h n m 1 is fixed and u > 0. Using a fixed point theorem for operators on a cone, we develop criteria for the existence of positive solutions of the boundary value problem for u on a suitable interval.     

On the global convergence of a generalized iterative procedure for the minisum location problem with ℓ p distances for p > 2

This paper presents a procedure to solve the classical location median problem where the distances are measured with ? _p -norms with p > 2. In order to do that we consider an approximated problem. The global convergence of the sequence generated by this iterative scheme is proved. Therefore, this paper closes the still open question of giving a modification of the Weiszfeld algorithm that converges to an optimal solution of the median problem with ? _p norms and ${p \in (2, \infty)}$ . The paper ends with a computational analysis of the different provided iterative schemes.     

Global L p estimates for degenerate Ornstein–Uhlenbeck operators

We consider a class of degenerate Ornstein–Uhlenbeck operators in ${\mathbb{R}^{N}}We consider a class of degenerate Ornstein–Uhlenbeck operators in \mathbbR^N{\mathbb{R}^{N}} , of the kind

A o ?i, j=1p0aij?xixj2 + ?i, j=1Nbijxi?xj\mathcal{A}\equiv\sum_{i, j=1}^{p_{0}}a_{ij}\partial_{x_{i}x_{j}}^{2} + \sum_{i, j=1}^{N}b_{ij}x_{i}\partial_{x_{j}}      12. Strong summability theorems for H p (Δ d )      Ushangi Goginava  Larry Gogoladze 《Acta Mathematica Hungarica》2013,138(3):259-266 We prove that certain means of the (C,α,…,α)-means (α=1/p?1) of the d-dimensional trigonometric Fourier series are uniformly bounded operators from the Hardy space H p to H p (1≦p≦2). As a consequence we obtain strong summability theorems concerning (C,α,…,α)-means.      13. Regularity for minimizers of functionals with p – q growth      Luca Esposito  Francesco Leonetti  Giuseppe Mingione 《NoDEA : Nonlinear Differential Equations and Applications》2009,6(2):133-148 We prove higher integrability for the gradient of vector-valued minimizers of some integral functionals with p – q growth. Received February 9, 1998      14. Martingale hardy spaces for 0<p≦1      F. Weisz 《Probability Theory and Related Fields》1990,84(3):361-376       15. Daugavet type inequalities for operators on L p–spaces      Schep  Anton R. 《Positivity》2003,7(1-2):103-111 Let T be a regular operator from L p L p. Then , where Tr denotes the regular norm of T, i.e., Tr=|T| where |T| denotes the modulus operator of a regular operator T. For p=1 every bounded linear operator is regular and T=Tr, so that the above inequality generalizes the Daugavet equation for operators on L 1–spaces. The main result of this paper (Theorem 9) is a converse of the above result. Let T be a regular linear operator on L p and denote by T A the operator TA. Then for all A with (A)>0 if and only if .      16. Regularity for minimizers of functionals with p – q growth      Luca Esposito  Francesco Leonetti  Giuseppe Mingione 《NoDEA : Nonlinear Differential Equations and Applications》1999,6(2):133-148 We prove higher integrability for the gradient of vector-valued minimizers of some integral functionals with p – q growth. Received February 9, 1998      17. On the gibson barrier for the pólya problem      G. Dolinar  A. E. Guterman  B. Kuzma 《Journal of Mathematical Sciences》2012,185(2):224-232 We study lower bounds on the number of nonzero entries in (0, 1) matrices such that the permanent is always convertible to the determinant by placing?±?signs on matrix entries.      18. Unconditional structures of translates for L p (ℝ d )      D. Freeman  E. Odell  Th. Schlumprecht  A. Zsák 《Israel Journal of Mathematics》2014,203(1):189-209 We prove that a sequence (f i ) i=1 ∞ of translates of a fixed f ∈ L p (?) cannot be an unconditional basis of L p (?) for any 1 ≤ p < ∞. In contrast to this, for every 2 < p < ∞, d ∈ ? and unbounded sequence (λ n ) n∈? ? ? d we establish the existence of a function f ∈ L p (? d ) and sequence (g n *) n∈? ? L p *(? d ) such that \({({T_{{\lambda _n}}}f,g_n^*)_{n \in {\Bbb N}}}\) forms an unconditional Schauder frame for L p (? d ). In particular, there exists a Schauder frame of integer translates for L p (?) if (and only if) 2 < p < ∞.      19. On some properties of generalized solutions of the wave equation in the classes L p and W p 1 for p ≥ 1      V. A. Il’in  A. A. Kuleshov 《Differential Equations》2012,48(11):1470-1476 For each p ≥ 1, in closed analytic form, we establish the existence of a unique generalized solution in L p of the mixed problem for the wave equation in the rectangle [0 ≤ x ≤ 1] × [0 ≤ t ≤ T] with zero initial conditions and with boundary conditions of the first kind, one of which is homogeneous. Next, we derive necessary conditions for this solution to belong to W p 1 . We present examples showing that these necessary conditions are not sufficient for any p ≥ 1.      20. Lipschitz Continuity Properties for p−Adic Semi-Algebraic and Subanalytic Functions      Raf Cluckers  Georges Comte  François Loeser 《Geometric And Functional Analysis》2010,20(1):68-87 We prove that a (globally) subanalytic function ${f : X \subset {\bf Q}^{n}_{p} \rightarrow {\bf Q}_{p}}We prove that a (globally) subanalytic function f : X ì Qnp ? Qp{f : X \subset {\bf Q}^{n}_{p} \rightarrow {\bf Q}_{p}} which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a subanalytic family of functions fy : Xy ì Qnp ? Qp{f_{y} : X_{y} \subset {\bf Q}^{n}_{p} \rightarrow {\bf Q}_{p}} depending on p−adic parameters. The statements also hold in a semi-algebraic set-up and also in a finite field extension of Q p . These results are p−adic analogues of results of K. Kurdyka over the real numbers. To encompass the total disconnectedness of p−adic fields, we need to introduce new methods adapted to the p−adic situation.

Strong summability theorems for H p (Δ d )

We prove that certain means of the (C,α,…,α)-means (α=1/p?1) of the d-dimensional trigonometric Fourier series are uniformly bounded operators from the Hardy space H _p to H _p (1≦p≦2). As a consequence we obtain strong summability theorems concerning (C,α,…,α)-means.     

Regularity for minimizers of functionals with p – q growth

We prove higher integrability for the gradient of vector-valued minimizers of some integral functionals with p – q growth. Received February 9, 1998     

Daugavet type inequalities for operators on L p–spaces

Let T be a regular operator from L ^p L ^p. Then , where T_r denotes the regular norm of T, i.e., T_r=|T| where |T| denotes the modulus operator of a regular operator T. For p=1 every bounded linear operator is regular and T=T_r, so that the above inequality generalizes the Daugavet equation for operators on L ¹–spaces. The main result of this paper (Theorem 9) is a converse of the above result. Let T be a regular linear operator on L _p and denote by T _A the operator T_A. Then for all A with (A)>0 if and only if .     

Regularity for minimizers of functionals with p – q growth

We prove higher integrability for the gradient of vector-valued minimizers of some integral functionals with p – q growth. Received February 9, 1998     

On the gibson barrier for the pólya problem

We study lower bounds on the number of nonzero entries in (0, 1) matrices such that the permanent is always convertible to the determinant by placing?±?signs on matrix entries.     

Unconditional structures of translates for L p (ℝ d )

We prove that a sequence (f _i ) _i=1 ^∞ of translates of a fixed f ∈ L _p (?) cannot be an unconditional basis of L _p (?) for any 1 ≤ p < ∞. In contrast to this, for every 2 < p < ∞, d ∈ ? and unbounded sequence (λ _n ) _n∈? ? ? ^d we establish the existence of a function f ∈ L _p (? ^d ) and sequence (g _n *) _n∈? ? L _p *(? ^d ) such that \({({T_{{\lambda _n}}}f,g_n^*)_{n \in {\Bbb N}}}\) forms an unconditional Schauder frame for L _p (? ^d ). In particular, there exists a Schauder frame of integer translates for L _p (?) if (and only if) 2 < p < ∞.     

On some properties of generalized solutions of the wave equation in the classes L p and W p 1 for p ≥ 1

For each p ≥ 1, in closed analytic form, we establish the existence of a unique generalized solution in L _p of the mixed problem for the wave equation in the rectangle [0 ≤ x ≤ 1] × [0 ≤ t ≤ T] with zero initial conditions and with boundary conditions of the first kind, one of which is homogeneous. Next, we derive necessary conditions for this solution to belong to W _p ¹ . We present examples showing that these necessary conditions are not sufficient for any p ≥ 1.     

Lipschitz Continuity Properties for p−Adic Semi-Algebraic and Subanalytic Functions

We prove that a (globally) subanalytic function ${f : X \subset {\bf Q}^{n}_{p} \rightarrow {\bf Q}_{p}}We prove that a (globally) subanalytic function f : X ì Qⁿ_p ? Q_p{f : X \subset {\bf Q}^{n}_{p} \rightarrow {\bf Q}_{p}} which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a subanalytic family of functions f_y : X_y ì Qⁿ_p ? Q_p{f_{y} : X_{y} \subset {\bf Q}^{n}_{p} \rightarrow {\bf Q}_{p}} depending on p−adic parameters. The statements also hold in a semi-algebraic set-up and also in a finite field extension of Q _p . These results are p−adic analogues of results of K. Kurdyka over the real numbers. To encompass the total disconnectedness of p−adic fields, we need to introduce new methods adapted to the p−adic situation.