The Meda inequality for rearrangements of the convolution operator on the Heisenberg group Hn is proved. By using the Meda inequality, an O’Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operator MΩ,α and fractional integral operator IΩ,α with rough kernels in the spac...

This dissertation originates from a classical result that the `-stability of the convolution operator associated with a summable sequence are equivalent to each other for 1 ≤ p ≤ ∞. This dissertation is motivated by the recent result by C. E. Shin and Q. Sun (Journal of Functional Analysis, 256(2009), 2417–2439), where the `-stability of infinite matrices in the Gohberg-Baskakov-Sjöstrand class...

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

Recommended by Brigitte Forster-Heinlein For λ > −1 and μ ≥ 0, we consider a liner operator I μ λ on the class A of analytic functions in the unit disk defined by the convolution f μ −1 * fz, where f μ 1 − μz 2 F 1 a, b, c; z μzz 2 F 1 a, b, c; z , and introduce a certain new subclass of A using this operator. Several interesting properties of these classes are obtained.

In this paper, we introduce a linear operator for harmonic multivalent functions by using harmonic convolution operator and generalized Saitoh operator. We investigate some properties of a new subclass of harmonic multivalent functions defined by using this operator.

Keywords: Filter Modular space (Modular) filter convergence Rate of convergence Sampling operator Integral operator Urysohn operator Mellin convolution operator a b s t r a c t We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which...