In this paper Lq → Lp boundedness of integral operator with operator-valued kernels is studied and main result is applied to convolution operators.

The modified fractional integral operators, introduced in [4], are proved to be bounded from some Lp– space into some Lq– space with power-logarithmic weights.

Fourier multiplier theorems provides one of the most important tools in the study of partial differential equations and embedding theorems. They are very often used to establish maximal regularity of elliptic and parabolic differential operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensively in [1, 2, 3, 5, 7, 8, 9, 10, 11, 12 ]. B...

We consider the problem of recovering sparse vectors from underdetermined linear measurements via lp-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that two phenomena occur if p 6= 2. First, one may need substantially more than s log(en/s) measurements (optimal for p = 2) for uniform recovery of all s-sparse vector...

The Gentzen-Kripke construction of the semantics for intermediate logic LQ, which is obtainable from the intuitionistic propositional logic H by adding the weak law of excluded middle -*A v —• —1>4, is presented. Our construction spans the Gentzen system and the Kripke semantics for LQ by providing the way from the cut-elimination theorem to model-theoretic results. The completeness and decidab...

We introduce 2 parameter variants Lp,q of the Lebesgue spaces, to gain separate control on the asymptotic behaviour (p) and the local behaviour (q). Thus they behave w.r.t. p like the spaces lp and w.r.t. q like the spaces Lq on a probability space. Convolution behaves very well on those spaces.

For a complete measure space (X,Σ,μ), we give conditions which force Lp(X,μ), for 1 ≤ p < ∞, to be isometrically isomorphic to p(Γ) for some index set Γ which depends only on (X,μ). Also, we give some new characterizations which yield the inclusion Lp(X,μ)⊂ Lq(X,μ) for 0<p < q.

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.