and Applied Analysis 3 can be extended to a continuous mapping Tφ : L d → L d . One calls operator Tφ the L-multiplier operatorwith symbol φ. Theorem 1.4 Hörmander-Mikhlin . Let φ ∈ L∞ d have partial derivatives of order less than or equal to κ, where κ is the least integer strictly greater than d/2 (i.e., κ d/2 1). If, for some constant k > 0, ∀r > 0 ( ∀α ∈ 0 ) |α| ≤ κ ⇒ ∫ r/2≤|ξ|≤r ∣∣ ∣D ξφ ξ...

Over the past few decades, numerous studies investigated vigor and productivity of fruit species depending on rootstock which they were grafted, but exact size-controlling mechanism itself has not been fully elucidated, nor rapid selection methods defined. Thus, this study aimed to assess root anatomical characteristics their influence overall ‘Summit’ cherry tree confirm effect establish an ef...

and Applied Analysis 3 The final solution to problems in 1.3 can yield optimal lower and upper bounds of eigenvalues. Actually, from 1.3 , we have In ∥q ∥ ∥ 1 ) ≤ λn ( q ) ≤ Mn ∥q ∥ ∥ 1 ) ∀q ∈ L1, 1.4 which are optimal. Several extremal problems on Dirichlet, Neumann, and periodic eigenvalues of the Sturm-Liouville operator and the p-Laplace operator have been studied recently, where the potent...

In the early sixties, Amice ([Am1], [Am2]) studied the space of K-valued, locally analytic functions on Z Z p and formulated a complete description of its dual, the ring of K-valued, locally Q p-analytic distributions on Z Z p , when K is a complete subfield of C p. She found an isomorphism between the ring of distributions and the space of global functions on a rigid variety over K parameteriz...

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington Departamento de Fı́sica Aplicada, Universidad de Salamanca, E-37008 Salamanca, Spain Department of Physics, Science Laboratories, University of Durham, Durham DH1 3LE, United Kingdom Optics Section, Blackett Laboratory, Imperial College, London SW7 2BW, United Kingdom ~Received 20 December 2000; publis...