The evolution of a P system generates a tree of computation potentially infinite where it is very difficult to set the degree of closeness between two configurations. The problem is specially hard if we want to quantify that proximity in order to make useful comparisons. In this paper we propose some weak metrics on configurations of a P system with a fixed structure of membranes and briefly di...

Let L be a non-negative self-adjoint operator acting on 2 ( X ) , where is space of homogeneous type with dimension n . Suppose that the heat e − t satisfies generalized Gaussian p 0 ′ -estimates order m for some 1 ≤ < It known I + s i bounded ≥ | / and ∈ (see example, [5] [7] [9] [10] [13] [26] ). In this paper we study endpoint case = show weak is, there constant C > independent f so μ { x : ...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

The current paper establishes the sharp weak bounds of p-adic fractional Hardy operator. Furthermore, optimal type estimates for operator on central Morrey space are also acquired.