Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

Consider the linear parabolic operator in divergence form $$\mathcal{H} u =\partial_t u(X,t)-\text{div}(A(X)\nabla u(X,t)).$$ We employ a method of Dahlberg to show that the Dirichlet problem for $\mathcal{H}$ in the upper half plane is well-posed for boundary data in $L^p$, for any elliptic matrix of coefficients $A$ which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation $\partial_t u_\varepsilon(X,t)-\text{div}(A(X/\varepsilon)\nabla u_\varepsilon(X,t))$ in Lipschitz domains with $L^p$-boundary data.Comment: 21 page

Calder\'on-Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.Comment: 21 page

Oscillation of generalized differences of H\"older and Zygmund functions

In this paper we analyze the oscillation of functions having derivatives in the H\"older or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov's Law of the Iterated Logarithm. A better behavior is obtained for functions in the Lipschitz class via an interesting connection with Calder\'on-Zygmund operators.Comment: 16 page

Riesz-Jacobi transforms as principal value integrals

We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders express as principal value integrals against kernels having non-integrable singularities on the diagonal. On the other hand, we show that the Riesz-Jacobi transforms of even orders are not singular operators. In fact they are given as usual integrals against integrable kernels plus or minus, depending on the order, the identity operator. Our analysis indicates that similar results, existing in the literature and corresponding to several other settings related to classical discrete and continuous orthogonal expansions, should be reinvestigated so as to be refined and in some cases also corrected.Comment: 30 page

UMD Banach spaces and the maximal regularity for the square root of several operators

In this paper we prove that the maximal $L^p$-regularity property on the interval $(0,T)$, $T>0$, for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre type operators on $L^2(\Omega, d\mu; X),$ characterizes the UMD property for the Banach space $X$.Comment: 23 pages. To appear in Semigroup Foru

Transference of local to global L2L^2 maximal estimates for dispersive partial differential equations

In this paper we give an elementary proof for transference of local to global maximal estimates for dispersive PDEs. This is done by transferring local $L^2$ estimates for certain oscillatory integrals with rough phase functions, to the corresponding global estimates. The elementary feature of our approach is that it entirely avoids the use of the wave packet techniques which are quite common in this context, and instead is based on scalings and classical oscillatory integral estimates.Comment: 10 page

Implicaturas generalizadas de cantidad en el rendimiento de algunas formas y oposiciones del sistema verbal español

En el presente trabajo nos proponemos abordar la descripción de algunos aspectos del sistema verbal del español desde una perspectiva pragmática. En particular, indagaremos la explicación de algunos usos típicos de los morfemas temporales a partir de la entrada en juego de procesos inferenciales recurrentes generados por el principio Q o principio de cantidad propuesto por Horn (1984, 1988). Observaremos, bajo este punto de vista, el rendimiento de las oposiciones imperfecto / indefinido, indicativo / subjuntivo, pluscuamperfecto / pretérito perfecto / indefinido, indefinido / pretérito perfecto, y condicional / presente

Gramática cognitiva y enseñanza de la gramática de ele

La enseñanza de algunos aspectos especialmente escurridizos de la gramática de segundas lenguas puede beneficiarse de la concepción del lenguaje y los instrumentos descriptivos de este que ofrece la Gramática Cognitiva (GC) (Langacker).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Conocimiento que poseen los estudiantes de 4º de psicología sobre atención a la diversidad y el modelo inclusivo en el ámbito educativo

Este estudio pretende analizar el conocimiento adquirido por el alumnado de 4º de psicología sobre atención a la diversidad, los modelos educativos de integración e inclusión y las necesidades específicas de apoyo educativo que pueden presentar los niños durante su desarrollo; todo ello con el objetivo de asegurar que los actuales estudiantes de psicología, y futuros profesionales del ámbito educativo, dispongan de un conocimiento correcto; así, próximamente, las escuelas podrán disponer de profesionales bien formados que sean capaces de adaptar las enseñanzas didácticas a la situación de cada niño y de poder responder a sus necesidades educativas satisfactoriamente. Para ello, se realizó una recogida de datos a través de un instrumento cuantitativo creado ad hoc para analizar tanto el conocimiento adquirido por el alumnado de psicología sobre atención a la diversidad, como las posibles variables personales que pueden estar relacionadas con la calidad de dicho conocimiento. El análisis del conocimiento de los estudiantes muestra conclusiones positivas sobre este, aunque no se acerca del todo al modelo teórico; por otro lado, el análisis de las variables muestra una clara relación entre el conocimiento y la formación recibida, no existiendo dicha relación con la edad, el interés por la educación o la proximidad a personas con NEAE.This study aims to analyse the acquired knowledge by the students of 4th year of psychology about diversity awareness, integration and inclusion educative models, and the specific needs for educational support that can show some children through development; the main objective is to asure that current psychology students and future professionals of the educational field have the necessary knowledge. Consequently, the schools will have the opportunity to have well trained professionals that are capable to adapt didactic instructions to every child’s situation and to meet their educational needs sactisfactorily. To achieve this, we carried out a data collection with a cuantitative tool created ad hoc to analyse the acquired knowledge by the psychology students about diversity awareness, as well as personal variables that can be related to the quality of this knowledge. The analysis of the student’s knowledge shows optimist conclussions about this, although it hasn’t approached the theoretical model; on the other hand, the analysis of the variables shows a clear relationship between the knowledge and the received training, as well as no relationship with age, interest for education, or proximity to children that show specific needs for educational support.Universidad de Sevilla. Grado en Psicologí