Search

In this note we show that the integral means spectrum of any univalent function admitting a quasiconformal extension to the extended complex plane is strictly less than the universal integral means spectrum. This gives an affirmative answer to a question raised in our recent paper., Comment: The main results of this paper will be included in the preprint "Integral means spectrum functionals on Teichmuller spaces" arXiv:2405.07683

In this paper, we introduce and study the integral means spectrum (IMS) functionals on Teichmuller spaces. We show that the IMS functionals on the closure of the universal Teichmuller space and on the asymptotic universal Teichmuller space are both continuous. During the proof, we obtain some new results about the universal asymptotic Teichmuller space. We also show that the integral means spectrum of any univalent function admitting a quasiconformal extension to the extended complex plane is strictly less than the universal integral means spectrum., Comment: 26 pages

In this note we investigate the Prawitz's area theorem and establish a new univalence criterion for the locally univalent analytic functions in the unit disk, which generalizes some related results of Aharonov [Duke Math. J., 36(1969), 599-604]., Comment: 14 pages

In this paper we study a multiplier operator which is induced by the Schwarzian derivative of univalent functions with a quasiconformal extension to the extended complex plane. As applications, we show that the Brennan conjecture is satisfied for a large class of quasidisks. We also establish a new characterization of asymptotically conformal curves and of the Weil-Petersson curves in terms of the multiplier operator., Comment: Accepted by Bull London Math Soc

In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators. Also, for some special cases, we obtain the sharp estimates for the norms of certain Hilbert-type operators., Comment: Rocky Mountain Journal of Mathematics, to appear

In this paper we introduce and study several new Hardy-Littlewood-P\'olya-type operators. In particular, we study a Hardy-Littlewood-P\'olya-type operator induced by a positive Borel measure on $[0,1)$. We establish some sufficient and necessary conditions for the boundedness (compactness) of these operators. We also determine the exact values of the norms of the Hardy-Littlewood-P\'olya-type operators for certain special cases., Comment: Accepted by Journal of Applied Analysis and Computation

In this paper we introduce and study several new Hilbert-type operators acting between the weighted Fock spaces. We provide some sufficient and necessary conditions for the boundedness and compactness of certain Hilbert-type operators from one weighted Fock space to another.

In this note we study the generalized Hilbert series operator $H_{\mu}$, induced by a positive Bore measure $\mu$ on $[0, 1)$, between weighted sequence spaces. We characterize the measures $\mu$ for which $H_{\mu}$ is bounded between different sequence spaces. Finally, for certain special measures, we obtain the sharp norm estimates of the operators and establish some new generalized Hilbert series inequalities with the best constant factors., Comment: Filomat, to appear

In this note, we introduce and study a new kind of generalized Ces\`aro operators $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\mu$ for which $\mathcal{C}_{\mu}$ is bounded (compact) from one Dirichlet-type space $\mathcal{D}_{\alpha}$ into another one $\mathcal{D}_{\beta}$., Comment: Accepted by Acta Mathematica Scientia

The Tropical Rainfall Measurement Mission (TRMM) Microwave Imager (TMI) observed the Earth in lower latitudes between 1997 - 2015. Its conical-scan radiometer has nine channels and measured microwave radiances between 10 and 89 GHz. These data provide information on atmospheric temperature, humidity, clouds, precipitation, as well as sea surface temperature. Radiance data from other microwave radiometers such as Special Sensor Microwave Imager (SSM/I) and Special Sensor Microwave Imager Sounder (SSMIS) onboard various Defense Meteorological Satellite Program (DMSP) satellites are assimilated in clear-sky conditions in the Modern-Era Retrospective analysis for Research and Applications (MERRA) and its version 2 (MERRA-2) data sets at the Global Modeling and Assimilation Office (GMAO) at NASA Goddard Space Flight Center. The GMAO's Hybrid 4D-EnVar-based Atmospheric Data Assimilation System (ADAS) is enhanced with an all-sky microwave radiance data assimilation capability in the real-time GEOS-Forward Processing (FP) system. Currently, the FP system assimilates Global Precipitation Measurement (GPM) microwave imager (GMI) radiance data utilizing this all-sky capability, and is being extended to use more all-sky data from other microwave radiometers. In this presentation, we will focus on impacts of all-sky TMI radiance data on GEOS analyses of atmospheric moisture, precipitation and other fields, and discuss their applications for future GEOS reanalyses.